not sure reducing the deficit has any impact, or at least a controlling or direct impact, on reducing, maintaining current levels, or increasing inflation.

I do think reducing the amounts government insurers like Medicare and Medicaid pay for prescription drugs does have a direct impact on the CPI and accordingly "inflation" as it is popularly conceived. I think the Fed's interest rate hike does too. I think the current good news re Ukraine does too. (Things seem to be happening in a direction that favors Ukraine in the south, around Kherson, potentially jeopardizing Russia's fresh water sources to Crimea and in turn incentivizing Russia to seek peace)

Finally I think falling gas prices, probably not the result of anything any president does or doesn't do, tend to be anti-inflationary as well. The sum total of all of this, some of which is a credit to Biden, some of which isn't (but note the opposite side of the run-up was widely hailed by our board righties--and most of the rah-rah morons in the bottom intellectual half of the conservative media-- as "Biden's fault") is, I think, going to be anti-inflationary, just in time for the fall mid-terms.