A majority of Americans say President Barack Obama's support for and Mitt Romney's opposition against gay marriage won't affect their vote.

According to a The New York Times/CBS News poll released Monday night, 57 percent of respondents say Obama's support for such unions will not affect how they vote. Sixty percent say Romney's opposition is not a factor.

A greater number of people, however, said the move would make them less likely to vote for the president in the fall. Twenty-six percent of those surveyed said the president's position made them less likely to vote for him, while 16 percent said the shift in position increased the likelihood that they would vote for Obama.

Obama dropped his previous stance of “evolving” on the issue to come out in favor of legalizing marriage for gay couples last week in an interview with ABC News' Robin Roberts. The next day, the Obama campaign released a video contrasting the president's views with those of his presumed GOP rival, Mitt Romney.

A majority (67%) of those polled said they suspected Obama's announcement was made “mostly for political reasons.” Twenty-four percent said he acted out of principle.

Just 7 percent think gay marriage is an important issue in the election.