I am not an expert on this. All I can offer is opinion based on my flawed understanding of history.
One of the things that many Americans do not remember or choose not to take note of is that the USA was profoundly against our getting involved in WWII. Having been involved in WWI, we had become isolationist as a nation. The majority had no interest in what was happening 'over there' in Europe. Our political and military leadership tended to see things differently, and tried to sway US opinion towards going to war with Germany.
http://news.google.com/newspapers?i...q=uk+makes+final+payment+for+lend-lease&hl=en
We were willing to make war material and lend/lease it to Great Britain and later, the Soviet Union and other countries. Many saw it, or it was sold, as a way to AVOID going to war; give the UK the means by which to win themselves, without our entering into the war. Sell the material instead of giving it away, so that Germany could not consider it a 'de facto' entry into the war by proxy.
http://pqasb.pqarchiver.com/latimes...ghth+Day+Over+Lease-Lend+Measure&pqatl=google
Few Americans took note of the 'final payment' that the UK just made to the US for that material.
However, the UK seems to revel in this and fails to note that the 'final bill' was 4.4 Billion, written down the Truman Administration from 25 Billion dollars.
http://pqasb.pqarchiver.com/baltsun...BY+U.S.;+NEW+LOAN+$4,400,000,000&pqatl=google
As to the actual question...
I think a lot depends on what time-frame you look at it. By the end of the war, England was nearly spent. The Soviets sacrificed more men that the US, of course, without question. But they also were not at the top of their game anymore. The US, on the other hand, had a roaring economy, and the 'arsenal of democracy' was pumping out monstrous amounts of material, from ships being built and launched in record time to what appeared to be a nearly inexhaustible supply of manpower. As the end of the war approached, we were approaching the zenith of our military might.
I think part of the US attitude that 'we saved yer butts' comes from the final outcome. The US and the USSR dictated the final terms of Germany's surrender. We divided up the world between ourselves, for the most part. And many thought we were just being 'safe' when we granted the Soviets status as equals; they would certainly become that, but many, including Patton, wanted to turn on them militarily while we had the might to destroy them.
I think another part of the attitude that Americans have it the pride we have in not imposing monstrous penalties on our fallen foes. We see ourselves, rightly or wrongly, as having helped Germany (and later Japan) back up to their feet again, dusted them off, and shook hands. We saw ourselves as not just saviors of Democracy in the larger sense, but also the epitome of concepts like fair play, forgiveness, and redemption.
Did America save Britain? Well, if you look at it from the standpoint of the entire war effort, I offer a qualified 'yes'. Without lend-lease, I doubt that England would have stood indefinitely against Germany but who knows? If you do not include lend-lease but just the military effort of the US, then perhaps and perhaps not.
Let me say that
together, the US, the UK, and the USSR certainly stood against many, and we prevailed, and the world is a much better place because of it. In the USA, we have resources that the UK simply does not possess, due to our size, our manufacturing base (at the time) and even our American attitudes about bullies and what ought be done about them (again, at the time).
Who saved whom? We saved us. That's about all I can think is a fair statement.