Should Democrats complain about the large deficits that Trump and the Republicans are creating? Or is this playing into the Republican narrative that made the stimulus in 2009 inadequate and gave us austerity from then onwards?
The answer that mainstream economics gives is straightforward. In a recession when interest rates have hit their lower bound  you do not worry about the deficit and you ignore those that do worry. Deficits should be whatever size is required to enable the economy to recover. Enough stimulus so that central banks feel they need to raise interest rates above their lower bound. Politicians failed to follow that advice during the last recession.
In contrast, when the economy is not in a recession, and interest rates are perfectly able to control aggregate demand, then deficits at a level where government debt starts rising may well be a problem. For various reasons, not least the chance of a recession, it is best to have deficits at a level which very gradually reduces the ratio of government debt to GDP, unless you have a good reason for doing otherwise.
There are many reasons why, outside of a recession, deficits that, if sustained, would steadily increase the debt to GDP ratio may be bad for the economy, but let me give the most obvious here. For a given level of government spending, interest on debt has to come out of taxes. The higher the debt, the higher the taxes. That is a problem because high taxes discourage people from working, and it is also unfair from an intergenerational point of view.
This last point is obvious if you think about it. The current generation could abolish taxes and pay for all spending, including any interest on debt, by borrowing more. That cannot go on forever, so at some point taxes have to rise again. A whole generation has avoided paying taxes, but at the cost of future generations paying even more.
As a result, unless there is a very good reason like a recession , a responsible government will not plan to sustain a deficit over time that raises the debt to GDP ratio. The problem though is that it is very tempting for a government not to be responsible. The current US government, which is essentially a plutocracy, wants above all else to cut taxes for the very wealthy, and if they do it without at the same time raising taxes on other people but instead by running a deficit they think they can get away with it. Democrats have every reason to say that is irresponsible, although of course the main thing they should focus on is that the last people who need a tax cut are the very rich.
Unfortunately being responsible can seem rather dull and boring, so it may be tempting to hype things up a bit by predicting some disaster that will come from rising deficits. That is not a good place to go, because you are crying wolf. Large deficits are like overeating. Do it once or twice and you will survive. Do it every day and you will die young. The only difference from overeating is that you do not die young, but your children do.
So much for mainstream economics. What about MMT, which is often characterised as implying that deficits do not matter? That is an incorrect characterisation: what MMT actually says is that inflation should determine what the deficit should be. If inflation looks like staying below target you can and should have a larger deficit, and vice versa. The reason they say that is that they think the central bank, in changing interest rates to control inflation, is wasting its time, because they believe rates do not have a predictable impact on demand and inflation. If that were true, then even mainstream economists would agree that the deficit should be at whatever level keeps inflation at target. The difference between MMT and the mainstream is whether the central bank is or is not wasting its time.
In an important sense, whichever perspective you take, thinking about stabilisation policy or long run deficits can just muddy the waters when it comes to the Republican tax cuts. The reason that Republicans mainly fund tax cuts for the very wealthy by borrowing is that it appears this is not costing anyone anything. If nobody’s taxes are going up, the argument goes, why should we mind too much if the richer get even richer. The key point to get across is this. There are two possibilities. The first is that if it is possible to permanently cut some taxes forever without raising others or cutting spending, why should the tax cut not go to those who need it rather than those who don’t. The second more likely possibility is that it is not sustainable, in which case at some point tax paid by ordinary people will go up or spending on ordinary people will be cut to pay for tax cuts to the very rich. Either way, ordinary people are losing out. To focus on deficits or inflation just detracts from this basic truth.
 The lower bound is either where the central bank thinks it is or the point that interest rate cuts become an unpredictable and therefore ineffective instrument.
 A natural rather than man made disaster might be another good reason to run deficits. Public investment on high return infrastructure is another.