Depends on what time frame we're talking about. If the jet fighters had been available in '43 (and would have been if it wasn't for Hitler's infamous fighter bomber order) when they actually had enough oil to put sufficient numbers of them in the air, the allied bomber squadrons would have been in a world of hurt given it's 4:1 kill ratio. Its amazing to think though, they had such potential but were often held back by such bad management (if they hadn't persecuted the jews, many of whom were Germany's best nuclear physicists, they might have even had the bomb, who knows). Not many people in the top management positions even saw the potential for jet aircraft (Goering cutback the engine development program to just 3 dozen engineers in 1940) until it was too late.
The problem with that scenario is that, had it happened, the Glouster Meteor and P-80 would have been rushed through the final stages of development, be ready by late 1944, and both were better aircraft with safer, more powerful engines.
Also there were key problems with the German jets. They left distinctive blast marks on the runways, and required concrete runways (difficult to repair, natch) of a certain length. There was an Allied plan to close all jet airfields by successive heavy bomber raids if necessary. It never was, but daily visits by 100 B-17s/B-24s per airfield was envisioned and possible. Germany could not have produced enough jets to stop it. They could make the efforts of 8th Air Force costly, but they never had the ability to truly win a battle of attrition.
Could the US have had that many a-bombs by '47?
The scenario I describe is basically the one spelled out by US warplans circa the Battle of Britain. Having no further need to equip the RAF (who used about 30% of all US aircraft that came off the production lines), and having skipped B-17/B-24 production and headed directly to transoceanic bombers, further production efforts could and would have been devoted to the atomic bomb. The number sounds larger than it really is, as well, because it wasn't hard to build 2000 B-36s in WW2 America, and the buildup would not have been interfered with by combat losses. Assume the B-36s are ready for production by 1944. Six months to build them all. It takes until mid-1947 to build all the a-bombs.