—History also shows that keeping the money system small is what lengthened the biggest recession of the 20th century into the Great Depression. Expanding the amount of cash in circulation ameliorated the effects.
—When the housing bubble burst and the derivatives market crumbled, a lot of value (“money”) blipped out of existence. Are you taking this massive disappearance of money into account when positing that a huge influx of cash will cause inflation?
—Money that is hoarded in mattresses, or kept in savings accounts bearing miniscule amounts of interest, might as well not exist for all they factor into inflation. Inflation may kick in when people start spending again. And that won’t happen until people are working in jobs again. And that won’t happen until the economy recovers. And that won’t happen until (among other things) the value that disappeared in the crashes is restored.
—Part of the way the government expanded the amount of cash in circulation is by buying financial instruments (aka “bank bailout”.) When the economy recovers, they can recoup some of that money by selling what they bought, and blip that money out of existence the same way it came into existence (either by repaying loans, or by returning imaginary cash to the pixel compost pile). That will smallify the amount of cash in circulation at the time when it needs to be nulled out to keep inflation from climbing.
In short, to answer your question: not too much. Economic questions and economic systems are rarely as simple and one-sided as people think, especially people that would have us try Hoover’s economic recovery plan all over again.