Six in 10 Americans say President Obama’s embrace of gay marriage will have no impact on their vote this year, according to a new Gallup poll. But of the rest, twice as many say it makes them less likely to support the president.

Twenty-six percent of Americans in the poll said Obama’s switch on the issue makes them less likely to vote for him this November, compared to 13 percent who said it makes them more likely to support him.

The poll reflects the fact that the issue isn’t top-of-mind for most voters, but also the fact that it could pose some electoral problems for the president.

According to the poll, most of those who say they are now less likely to vote for Obama are Republicans (more than half of GOPers say this). But 10 percent of Democrats and 23 percent of independents say the same thing, which suggests the president could be turning off at least some key voters.

By contrast, just 2 percent of Republicans and 11 percent of independents say his position makes them more likely to support the president.

The question, though, is how many of those turned-off Democrats and independents either (a) weren’t going to support him in the first place, or (b) may be less inclined to vote for Obama but will still wind up doing so. Indeed, the fact that most Americans say this is a non-issue speaks volumes about its lack of importance to voters, and there’s no indication about just how much of an impact the issue has on voters who say it does matter.

We have long known that the enthusiasm on this issue resides largely on the anti-gay marriage side, and this poll reflects that. Even though a majority of Americans — 51 percent — say they approve of Obama’s decision (compared to 45 percent who disapprove), the fact is that supporters are significantly less avid than opponents.

While a strong majority of Americans says this issue has no impact on their votes, the fact that it matters to nearly 40 percent of Americans isn’t insignificant.

And if Obama forfeits some Democratic and independent votes in a tight race, that could matter.