Poll shows Mitt Romney with slight lead over President Obama, as Americans question Obama’s motive in backing gay marriage

Mitt Romney has taken a slim lead over President Obama, with two-thirds of Americans believing Obama endorsed same-sex marriage for political reasons, according to a New York Times/CBS News poll published Tuesday.

Romney holds a 46-percent-to-43-percent advantage over the president, but the Republican’s 3-point edge is within the survey’s margin of error. The monthly poll showed the two candidates tied in April, after Obama led in February and March.

The survey was conducted last week in the days after Obama became the first president to publicly back gay marriage.

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Most respondents downplayed the importance of the same-sex marriage debate in the general election. Fifty-seven percent said the president’s announcement will have no effect on their vote; 26 percent said they are less likely to vote for Obama, and 13 percent said they are more likely.

Only 7 percent said same-sex marriage is the most important issue in the campaign, placing it far behind the economy and jobs, at 62 percent, but ahead of foreign policy, at 4 percent.

But if a majority of Americans will not base their votes on gay marriage, most also do not believe Obama’s declaration was based on principle. Just 24 percent said they believe the president supported same-sex marriage because it is right; 67 percent said he did it for political reasons.