Breaking News: Trump said Iran has agreed to a deal and they just need to sign it. Oil futures?

Trump said Iran has agreed to a deal and only needs to sign it. During an Oval Office signing ceremony, he described it as major breaking news and suggested that once the issue is resolved, gas prices could fall below $2 per gallon.

Putting politics aside, if sanctions on Iranian oil exports were eased and additional Iranian crude entered the market, how much downward pressure could that realistically put on oil prices? Would U.S. purchases to refill the Strategic Petroleum Reserve (SPR) be large enough to offset a meaningful portion of that increased supply, or is the SPR simply too small relative to the global oil market?