Yes, the balance of federal spending to taxation impacts inflation.
you can have deflation alongside deficit spending and you can have inflation with a budget surplus. both are quite possible. and it isn't just because of lag time on the effects of fiscal policy. inflation doesn't care whether the budget is in surplus or deficit. it cares about some numbers related to that, but also specifically not that itself.
because it is not about measuring spending vs. taxes, it is about measuring spending vs. the capacity of the economy to meet the demands of that spending. reducing taxes means there are more POTENTIAL competitors bidding for the economic output, not necessarily more ACTUAL competitors for it. Understand?
That is why certain types of taxes tend to have much less effect on aggregate demand than others; why reducing top income tax rates is usually not at all effective as a Keynesian stimulus (it tends to just get saved as compared to tax cuts for lower incomes) and also why they don't tend to cause much (if any) inflation either-- which is why going from Eisenhower's tax rates to Reagan's didn't cause a massive change in how the economy works despite Eisenhower's income tax rates sounding like communism to 21st century ears.
It is important to keep in mind that when economists speak of these things it's always at best an approximation because it is inherently a prediction of human behavior, which is always going to be fuzzy. When an economist says something like "tax cuts are good for growth" and you correctly observe that idea depends on whether the economy is already at full employment or not, that observation you would have just made is still an oversimplification. tax cuts mean there is more money that
can be used by the private sector to buy things, but that only matters if it
actually is used to buy things.
So what do tariffs do? They reduce the amount of goods from abroad that people can buy for the same price by destroying some of the money spent whenever it is spent in that manner. In terms of the effect of this on inflation, what have we accomplished by a tariff? If inflation is supposed to be an analog of the Federal budget balance, then we should think it allows the Federal government to spend more precisely by how much 'revenue' is claimed by the tariff in order to have the same inflation as otherwise.
But why would that be the case for a tariff?
Simple, you might think:
The tariff reduced the consumption of foreign goods, which means there is less currency abroad to demand exports from our economy and therefore more output available for the government to make use of.
But... it also may mean that there is more consumption of domestic goods, since they are comparatively cheaper now, meaning there is less local output available for the government to make use of.
Which of these factors is greater? It depends on a lot of things. Simplistically, it depends on price elasticities of demand and supply. But even that is just a way to model it.
And this is before even considering whether what the government wants to buy with its spending has the same inputs as the goods that were tariffed or their domestic counterparts (or whatever someone might have bought instead of buying the tariffed good).
In the long run, you might say, everything economical is ultimately a matter of the sum total of human effort, and putting tariffs on some goods while spending government monies in others means nudging the way that human effort is organized in a direction away from the production of the tariffed goods and toward more of the production of whatever the government spent its money on-- or which is to say, in the long run everything actually does all have the same inputs because everything an economy produces is ultimately put together or gathered or harvested by humans doing labor, and the capacity of humans generally to produce one thing or another (i.e. by education and training) responds to price signals. But of course that takes awhile. And is subject to its own complexities. But
theoretically...
Do you not see how woolly this is getting compared to the logic of an accounting balance? It is all very flimsy and if you wanted to model it, each of these factors would have (and need) a different coefficient. Whereas an accounting balance is a straightforward matter of addition and subtraction and you either have enough or you don't. How a tariff or any other tax effects inflation (if it does at all) is anything but that. And I just want to stress this again: inflation doesn't care at what point the accounting balance would be $0. The effect of additional spending does not have an inflection point there. The effect of additional taxes does not have an inflection point there. Because it's fundamentally not about that.