If the US was able to survive the loss of the Vietnam war and the Bay of Pigs where many people who bet their lives on the US died after being abandoned by them, the US will survive this as well and American credibility will be just fine in the long term.

Basically, the rest of the world will have to learn that getting the US to agree to something that is opposed by a significant group of Americans is a losing proposition. The fact that the Paris climate pact was not even submitted for ratification by the Senate, should tell you that there was significant opposition.