I am not familiar with how nuclear weapons developed and how fast you could produce them, but "Fat Man" and "Little Boy" didn't cause more damage than the firebombing of Hamburg, Dresden or Tokio. These were not the nuclear weapons of the cold war. Hiroshima and Nagasaki are still two densely populated cities. These bombs did not turn these cities into Chernobyl.
Also: apparently 1930 Me262 were produced, but only 1433 were taken into Luftwaffe-service. Most of them were destroyed or damaged in transport, usually by allied aircraft who at that time could roam free. Only 100 were operational at a time, 232 were lost to enemy fire, 727 lost in accidents, and according to most sources I found only 100 were shot down. Inexperienced pilots were a major problem. The lack of fuel did not only keep the Me262 on the ground, in prevented adequate training. And apparently the R4M-rockets were very effective against bombers. In Ziegler's "Hitler's Jet Plane: The ME 262 Story" you can read that on march 18, 1945, 6 Me262 engaged 1221 bombers and 632 escort fighters. During the battle, the Me262's launched 144 R4M-rockets. Result was that 25 bombers were lost, for just 2 Me262. Now imagine what 60 would have caused, and this happening more often.
This is just ONE factor. Imagine them being able to train their pilots better and more of them being in the air. What makes you think that "Germany could have only won if the allies would have let them"? Stop underestimating the Wehrmacht. The Wehrmacht 1944 was never fully operational because of the severe fuel shortage, and low morale because of the lack of air support. This lack of morale led to millions of them surrendering without a fight. The western allies took about 7-8 million POWs between the landing in Normandy and the 8th of may 1945, the soviets 2-3 million. Imagine these 10 millon men putting up a real fight. You probably would have had Verdun/Somme instead of the Falaise Pocket. I don't think the American public would have accepted such losses. And sorry, I don't see the American military as this epic fighting force, their wars since 1945 don't indicate that at all. The western allies ability to build bombers and willingness to waste them also wasn't unlimited. These atom bombs were probably very expensive and time consuming to produce. They would have to transport them by ship, unless they produce them in Britain, and a lot of them would get lost at sea.
Most people seem to assume that time was running for the allies. But was it really? Prolonging the war could have made the German army an even better fighting force. The Luftwaffe was about to limit their production on the Bf109, Me262, the Ta152, the Do335, and the Ar234. I might have forgotten one. But these were formidable aircraft, and they wouldn't be rendered obsolete that fast.
At sea the Germans were in a similar situation. They had just developed the Type XXI and XXII-submarine. These submarines were advanced enough for the French to use them until 1969 and Western Germany until 1982. Both the US and the USSR build submarines that were heavily influenced by them. They were also relatively inexpensive to make, compared to the other types.
On land you had the famous Sturmgewehr and the MG 45. The MG 45 could be produced in 60% the time required for an MG 42. Same goes for the STG 45, compared to the STG 44. They also just had the Panzerfaust 150, and were close to fielding a wire-guided air-to-air- and portable wire-guided anti-tank missile, the Ruhrstahl X-7. Nobody knows how effective they would have been, but the design was later refined by the french and sold as the NORD SS-10. The Israeli's in one of their wars used them against arab tank armies and reported about 66% hit probability in a combat situation against moving targets with only little practice required. It was designed to be inexpensive. They also were close of developing their own proximity fusze. The proximity fuze was one of the most important weapons of the western allies, it makes anti-aircraft fire and artillery fire much more effective.
I am not talking about Nazi spacecraft here. These are weapons that at the end of the war already existed, but hadn't been used yet in any significant numbers.
They also had just executed people like Canaris, his co-conspirators, and about 2000 other suspected traitors, spies, resistance members or whatever you want to call them. Canaris was the chief of the German military intelligence service Abwehr and a British agent. According to the testimony of the former Abwehr-officer and -resistance member Lahousen at the Nuremberg trials, Germany's own military intelligence service was leaking all kinds of secret information to the British. A fun topic to research is how often German aircraft with new technology accidentally landed on British airfields, totally undamaged, so that the British can study them. When the British were having trouble with the new Fw190, a pilot accidentally landed his fresh-out-of-the-box Fw190 on a British airfield. The British could then study it's design, strengths, weaknesses. Now maybe this can happen by accident, but in case of the Lichtenstein-radar, it clear what was going on there:
I just quote Wikipedia, auto-translated:
So the German night fighters were giving the British a hard time, then...
In April 1943 a Ju 88 C-6 equipped with a FuG 202 B / C had landed in England, the British learned details about the German aircraft on-board radar. From analysing the wavelength they could adapt in the length of the aluminum strips (called Dübbel in German, Window in England) with which the FuG 202 B/C could be jammed. This made the on-board radar system largely useless for a few decisive weeks.
[...]
Late in 1943 the Luftwaffe began using the improved FuG 220 Lichtenstein SN-2 which operated at the lower 90 MHz frequency at the lower end of the VHF broadcast band. The device was far less sensitive to electronic jamming measures.
[...]
On April 28, 1944, a Bf 110 with the registration C9+EN with the Lichtenstein SN-2 radar landed at Dübendorf Airport in Switzerland after being blinded by headlights that could not be shaken off.[2] The radar was immediately examined by ETH specialists, including in field tests, in which the aircraft was pulled onto a ramp to point the radar in the air.[3] After the German side had also considered an attack on Dübendorf, it was agreed to destroy the aircraft under German supervision. [...]
On 13 July 1944 the improved version of the SN-2 fell into Allied hands after a fully equipped Ju 88 G-1 accidentally landed at RAF Woodbridge in south-east England due to a navigational error. The crew noticed the error too late; she didn't have time to destroy the radar and the friend-or-foe detection device ("Erstling"). Also on board this Ju 88 was the FuG 227 Flensburg, previously unknown to the Allies, for targeting emissions from the Monica radar installed in British bombers. This crew error resulted in the immediate shutdown of all Monica radars and the blocking of some of the SN-2's frequency bands.
Ok, three times? That is not a coincidence. For more of these look up "Oslo Report" for example.
The fact that no Me262 accidentally landed on a british airfield might be connected to the purges after the failed July 20th-plot. So another thing which probably would have strengthened them.
Anyhow. I think many factors contributed to the ultimate outcome of the war, and oil is one of the biggest, if not the biggest. I don't see makes people think the allies would have steamrolled them, no matter what. The "Wunderwaffen" was not just something Hitler fantasized about in his bunker, there was some really good stuff that was just about to get fielded.