What if both embassies were overrun and while Carter was debating what to do the Russians set up a rescue operation for both embassies.
Say they are somewhat successful and 80% of the Russian hostages survive and 95% of the Americans (the Iranians were not expecting anything with the Americans and their guard was down).
How would the US government react when Russia just made Carter look like he didn't have the balls to confront Iran and get the hostages back.
Such was the nature of Cold War rivarly that I find it hard to imagine one side doing that kind of a favour for the other, even as an act of passive-aggressive, backhanded, faux-generosity. More likely, the USSR would just get their people out, and sit back and wallow in the USA frustration at not being able to do the same.
That said, if it DID happen, yes, it would probably be a pretty major embarrassment for Carter, though his Republican enemies might be a little tempered in their response, for fear of appearing to praise a Soviet operation. They would probably stop just short of adding "like the Russians did!!" when bellowing out their list of what actions they think Carter should have undertaken.