The declaration has little effect on the US. I mainly took the drama over it as 4D chess to defund the UN. If Trump really cared about the vote, he would have lobbied at least Japan and SK. And maybe he did and they voted the way he wanted them to.
I don't think we would or should completely back out, just get better results for our involvement. The blame? Nah, the credit would go to Trump if he could balance our contributions with the country's interests.