That doesn't follow. It's a reason to believe prices will increase, not that prices will increase roughly in line with the income increase. This distinction is not a minor detail, it's pretty crucial. If you give people $3k and the prices go up by $2k... that's a very different scenario from one where the prices go up by $3k.
As long as we’re in a deficit, spending for this program would directly increase the money supply. Of course there are other factors like velocity of money and elasticity of good/services but at the end of the day we’re increasing the amount of money (aka cash + credit) with no change to supply AND we’re going into debt to do it.
