No, "deficit" is not the same as "use the printing press instead of taxes"
If the money being spent was borrowed, then it wasn't produced by the "printing press" and doesn't cause inflation. The lenders reduce their consumption (or keep it reduced) while the borrowers spend the money or consume, so there's no inflation.
But if the money is increased by "printing" it, then there's only increased spending and inflation, and no reduced consumption, no new debt.
The quantity theory of money makes assumptions which are not present in the real world, i.e. that the velocity of money remains constant, employment is full, the economy is at full productive capacity.
You're misstating the quantity theory. It does not deny that there are the other factors. The quantity theory in itself is correct in saying that if the amount of money circulating is increased, all else being equal, then the prices increase. It states that an increase in quantity per se leads to higher prices/inflation. But it does not deny that this can be offset by other factors.
None of these conditions hold in the real world.
The quantity theory does not say these conditions always hold. These conditions do sometimes exist and sometimes not, but whether they do or not, increasing the money quantity in itself as an additional condition does increase the inflation above what it would have been had the money quantity not been increased. But with the other conditions also added to the mix, the inflation can be offset, or can go one way or the other. The quantity theory never said that the money quantity is the only factor which influences inflation.
If there are sufficient goods and services to absorb the spending, it won't cause inflation.
It will cause the inflation rate to be higher than it would have been otherwise.
Not to mention, yet again, that when running a trade deficit, the only way the private sector as a whole can increase its financial assets (cash, treasuries, money) is if the govt spends more than it taxes back.
That's snake-oil economics. The economists ("economists"?) who advance that theory are a tiny fringe who are just on a crusade for protectionism and are paranoid about the trade deficit (e.g., Peter Navarro, Steve Bannon). Most economists don't accept that theory.
Also, that theory is refuted by the experience of the late 1990s when the trade deficit soared to record high levels and yet the federal deficit went down to zero. There is no empirical data or sound economic theory connecting higher trade deficit to higher budget deficits.
Or, if there is any causal relation at all, the evidence is that
the higher federal deficits cause a higher trade deficit. This is indicated by the history after 1930, at which point the federal deficits were greatly increased, and as this continued mostly uninterrupted through later decades into the 80s and 90s, the trade deficits began and increased. So the order was
first --- New Budget Deficits, followed by
second --- New Trade Deficits
A > B. I.e., what happens first causes what happens second.
If you understand cause-and-effect, this means it was the new federal deficits which caused the later trade deficits. Not the other way around. But also there may be no causal relation at all.
The deficit and national doomsayers doomsayers have been yammering forever, but it hasn't happened.
What hasn't happened? There is damage caused by these higher and higher federal deficits.
If you think there is no damage, then why not increase the annual deficits to 4 trillion $$$ to pay the entire federal budget? You are refuted by your refusal to address this question. If you have any reason to say there is no damage from Trump's trillion-dollar deficit, you'd have to say the same for a 4-trillion-dollar deficit. Or any amount. You have no logic to explain why it's OK to run up the debt by 1 trillion per year, but not OK to double it (or triple or quadruple it).
Your only reasoning is that the higher debt now gives us instant gratification, so let's do it, no matter what harm it will do later.
But this all missed the point - the difference between nominal and real resources. If the real resources are available, financial or fiscal constraints are self imposed.
So, NO FISCAL RESTRAINTS is your bottom line. So again, why not run up the annual deficit to 4 trillion, to pay the whole federal budget?
(Your phrase "If the real resources are available" is meaningless. There's always "real resources.")
The fiscal restraints are imposed by the condition that we don't want to inflict future harm onto the economy i.e., onto people. Of course you can imagine almost any unrestrained borrowing and spending now, for a year or 2 or 3, and perhaps a net short-term gain, more "jobs" or "growth" etc., for each additional billion/trillion borrowed, but the damage occurs later when those debts have to be repaid, and then the only way to repay it is to run up still more debt, and then more and more, with no end.