When ministers, in response to demands for more public spending, declare there is no magic money tree they are in literal terms lying. One of the things that make governments that use their own national currency quite different from households is their unique ability to create money. This is no great economic revelation, as it has been taught to first year economics students for as long as there were first year economics students.
There is a very simple relationship between spending, taxation, borrowing and money creation. If we include paying the interest on its debt as part of government spending, then we can express that relationship in the form of an equation:
Government spending - taxes = new borrowing + new money creation
A great deal of confusion in popular writing about macroeconomics can be avoided if you just remember that equation. It is an identity, which means that no causation is involved. Governments are free to choose three of these four quantities, but not all four because the identity (the government’s budget identity) must hold. 
When economists say that higher government spending is paid for (or funded by) higher taxes or more borrowing, they are simply talking about how this identity is satisfied. Equally when politicians say we cannot afford to spend more on the NHS, they mean they are not prepared to raise taxes, borrow more or create more money.
Economists from the MMT school of economics are fond of pointing out that if the government chooses to increase spending but does nothing else, then this spending will be paid for by creating more money. However the practical relevance of this statement is zero, beyond confirming that the government can create money. This is because governments will generally respond to higher spending and that additional money creation by either increasing taxation or borrowing more.
Why is this? What stops UK governments making themselves very popular by increasing spending on the NHS, education and so on and paying for it by creating money? The short answer is that at some point this would become inflationary. Economists sometimes talk about this type of inflation being caused by too much money chasing too few goods. But my own view (and a monetarist might disagree) is that talking about too much money is again misleading. What causes the inflation is that the government has increased its demand for goods (produced domestically) or workers, the domestic private sector sees no reason to reduce their demand, and there is a limit on how many goods or workers can be provided (domestically). What really causes inflation in this case is not excess money creation but the aggregate demand for goods (or workers) exceeding the aggregate supply.
Why is this a better way of thinking about this type of inflation?  The most basic reason is that the problem would still arise if the government didn’t pay for the higher spending by creating money, but instead by borrowing from abroad. We would still at some point get excess aggregate demand for domestically produced goods or workers, and inflation would rise.
All this suggests that what limits aggregate government spending is the amount of goods the domestic economy is willing to supply, sometimes called productive capacity.  This is also a popular conclusion of the MMT school of thought. As Josh Ryan-Collins writes in the News Statesman: “The main constraint on public spending should be whether the economy has the productive resources and capacity to absorb such spending without it leading to excessive price rises.”
Thinking about things this way has its uses. It shows, for example, why in a recession there is every reason for governments to increase their spending, and finance this by raising borrowing or creating money. A recession is generally where there is an excess supply of goods and/or workers, so using those resources to produce stuff not only reduces unemployment (of machines and/or workers), but also makes everyone better off because they can benefit from higher government spending. Alternatively governments can keep spending unchanged but cut taxes in a recession, and this will not be inflationary.
This shows why deficit limits in a recession are a dangerous form of economic nonsense. Again this is no great economic revelation, but has been understood by economists for 80 odd years. If in the (very unlikely) event that governments cannot cover the extra spending or reduced taxation by borrowing, they can create money and this will not be inflationary, because there is an excess supply of goods and/or workers. That this basic macroeconomic truth was briefly ignored in many countries from 2010 onwards is a subject on which I once wrote a great deal.
Despite all this, it is not the case that productive resources and capacity are the main constraint on the amount government’s spend. Governments can spend more by persuading the private sector to spend less. In modern economies it can do this in two main ways. The first is by raising taxation. Suppose we start from a position where there is no excess aggregate supply or demand, so inflation is constant. The government can still spend more if it encourages the private sector to spend less by raising their taxes. 
The second way governments can reduce the private sector’s demand for goods is by raising interest rates. Higher interest rates encourage people to save more and spend less, making way for additional government spending without raising inflation. In countries with independent central banks targeting inflation this will happen because the central bank wants to keep inflation constant.
This second way of governments being able to raise spending (or cut taxes) raises a potential political problem in countries with independent central banks. Irresponsible governments may be tempted to raise their spending or cut taxes in popular ways (particularly before an election), pay for it by higher borrowing, and avoid the inflationary consequences because central banks raise interest rates. Higher interest rates might be unpopular with some (borrowers), but they will be popular with others (savers), and in any case it may be the central bank that gets the blame rather than the government.
Something along these lines seems to have happened in many countries from around the 1970s onwards, after the collapse of the Bretton Woods system of fixed exchange rates when interest rates began to be used routinely for controlling inflation. This is known as deficit bias, and is why some countries adopted either fiscal rules for the size of government deficits or debt, and or fiscal councils like the OBR. It is important to understand that these fiscal rules would be unnecessary if governments were responsible, and that the harm that deficit bias does is long term, minor (raising interest rates higher than they need be) and largely irrelevant in the current era of very low long term interest rates. The idea that deficit targets somehow limit the amount governments can spend or tax year to year is economic nonsense, but that doesn’t stop some governments and many in the media pretending otherwise.
This second way that governments might provide room for additional spending is hardly discussed by MMT economists, because they believe fiscal policy (or other measures) rather than interest rates should control inflation. If governments followed MMT and did this, then there would be no need for deficit targets. But nearly all governments nowadays do not do this, and have independent central banks controlling inflation (when they can) by varying interest rates.  As a result, as long as this is the case, appropriate deficit targets  have some place, but this place should never get in the way of fighting recessions or climate change.
In attacking the nonsense of analogies relating government finance to household budgets, MMT is on the side of the angels. But you do not need a new school of macroeconomics to do this, as the nonsense can, and was, easily exposed using either longstanding or more recent mainstream macroeconomic ideas and evidence.
In addition, when MMTers say that deficit targets are pointless, it is important to understand that this follows directly (and obviously) from their main departure from how most mainstream macroeconomists view demand management, which is a belief that fiscal policy rather than interest rate changes should manage aggregate demand in order to control inflation (outwith the lower bound for interest rates. At the interest rate lower bound, I think most mainstream macroeconomists would agree that fiscal policy has to take monetary policy’s place.)
Finally, MMT also favours combining fiscal stabilisation policy with keeping interest rates very low. If, as the evidence strongly suggests, higher interest rates reduce aggregate demand, then (outwith the lower bound) mainstream macroeconomic policy would allow more government spending for given levels of taxes or borrowing (or any other policy instruments) than an MMT policy would allow. This is because higher interest rates would reduce aggregate demand, making room for more government spending without increasing inflation. In this sense MMT’s choice of fiscal policy rather than interest rates for macroeconomic stabilisation lowers rather than increases the amount governments can spend.
 I now prefer to call this an ‘identity’ rather than a ‘constraint’ because it is not a constraint on spending, taxes or borrowing, precisely because governments can create money. Contrast this with a household’s budget constraint, where the money creation is not a legal option. But this is just language, not economics.
 Excess aggregate national demand is not the only reason national inflation can increase, of course. It can increase because of higher imported prices, such as the price of commodities like oil or gas.
 Productive capacity can also be a misleading term, because it suggests some kind of maximum for what the existing workforce and capital stock can produce. In reality most firms like to keep spare capacity in normal times to cope with unexpected but short term fluctuations in demand. The key measure is what firms are willing to supply at current rates of inflation.
 How much taxes need to rise depends on how permanent the tax increase is believed to be. If it is believed to be permanent, then taxes need to rise by about the same amount as the additional government spending. However if people believe the extra taxation is temporary, they may be tempted to pay some of the taxes from reduced savings. In this case the rise in taxation would have to be greater than the increase in spending to keep aggregate supply and demand in balance.
 For why most macroeconomists still think that, outwith the lower bound for interest rates, independent central banks using interest rate changes, rather than governments using fiscal policy, should control inflation see here.
 Unfortunately many deficit targets are badly formulated, and a bad fiscal rule can be worse than none at all. This is particularly true in the Eurozone, where national interest rates cannot control national inflation and so fiscal policy should, but this is made more difficult by deficit targets.