Monetary inflation that is not spent into the economy will not result in price inflation, or asset inflation for that matter. If the coins are held by the Executive or used to pay off debt held by the Federal Reserve, the new money won't enter the economy. Where things would get "interesting" is if the coins were used to pay off privately held debt (then that money would have to find somewhere else to be parked), but that would directly affect asset prices rather than consumer prices.
I for one think it would be great if the Executive/Legislature took back some monetary creation responsibilities from the Federal Reserve. We've had massive monetary expansion over the past few decades, but due to the way the Federal Reserve creates new money, it has chiefly resulted in asset inflation (hence "line always goes up") while actually squeezing the productive economy.
The real hazard of minting too much new money that sits around is that when a spendthrift Republican gains power, they might spend it all to recreate this "debt ceiling brinkmanship" dynamic for their kayfabe of fiscal responsibility - in a way that the effects don't show up until a Democrat is in office of course.
I don't understand how it would change anything about prices. The Federal Reserve already sets the interest rates indpendent of the deficit. Congress already has the ability to adjust the budget and pass laws to change spending, or increase/reduce taxes. The CBO already gives Congress estimates for every law and it's effect on the deficit.
Get ready for your $250 cup of coffee, and 20%+ interest rates forever if they do that.