In a system with a central currency controlled by a central bank that adjusts the money supply in tandem with commerical banks, there is effectively no deficit, only a tax on savers.
Each time the money supply is increased, the value of the dollar decreases by the proportion of the increase to the whole. By inflating the number of dollars, it decreases the value of a single dollar.
So if there were 10 total dollars, and you had 1, that one bill is worth 1/10th of the money. If a new dollar is created, and you still have 1 dollar, your dollar is now worth 1/11 of all the money, not 1/10th, a decrease of about 9%.
When the government runs a deficit and finances it by using the central bank to finance and roll over the debt, the value of the debt (and all other currency) decreases proportionally. In the above example, if I owed you a dollar, and you had a dollar, after expansion I pay you back, the dollar you received is worth 9% less than dollar that was lent. In effect, I have paid a 9% tax on my investment.
In the real world, this has a few really clear effects:
Inflation will exceed the "target" rate set by the Fed. This is a given that everyone knows happens. It's why living standards are stagnant and/or declining, even though the economy is "growing". In dollar terms, it's growing, but in economic output terms, it's not changing much.
Foreign debts will continue to be worth less and less, and eventually this will pressure foreign governments to switch, when possible, to other reserve currencies that have less inflationary pressure. For the time being, there isn't one.
US living standards will continue to erode, slowly, slowly, slowly and the middle and lower classes will continue to be pinched and experience lower than expected levels of economic success.