Can we believe the polls that say a big majority of Americans oppose the Supreme Court's decision in Citizens United?

No, because the people surveyed mostly only knew about the case from the description given by the pollster. Here's the way ABC/Washington Post tried to get its unprepared respondents up to speed:

Changing topics, do you support or oppose the recent ruling by the Supreme Court that says corporations and unions can spend as much money as they want to help political candidates win elections? Do you feel that way strongly or somewhat?

What percentage of those surveyed do you think understood "spend" to exclude contributing money to the candidate?  20%? I'm saying 20% to be snarky, because that's the proportion of respondents who approved of the decision. My real point is, the survey is utter trash. Worse than utter trash, because it propagated misinformation.