AUGUSTA, Maine — Polls showing support for same-sex marriage could be misleading, a veteran pollster warned Wednesday as he released his own survey showing strong support for Question 1.

Also Wednesday, former NFL Commissioner Paul Tagliabue and his family announced they had donated $50,000 to Mainers United for Marriage, the group leading the campaign to pass Question 1.

Contradictory responses to inquiries about attitudes toward same-sex marriage led pollster Patrick Murphy of Pan American SMS Group to conclude that the results of his and other recent polls might reflect artificially high support for the Nov. 6 ballot initiative to legalize gay marriage.

Results of a Pan American SMS Group Omnibus Poll of 400 likely Maine voters released Wednesday show 55.3 percent of respondents said they would vote yes when asked, “Do you want to allow the state of Maine to issue marriage licenses to same-sex couples?” Another 1.3 percent of respondents said they leaned toward a yes vote.

That compares to 38.5 percent who answered no to legalizing same-sex marriage, with another 0.5 percent indicating that they leaned toward a no vote.

However, responses to a preliminary question that asked those polled to describe their personal position on same-sex marriage raised doubts and spurred Murphy to include an analysis that states, “The percentage of those who say they plan to vote for same-sex marriage may well be inflated and in all likelihood is not at the level recorded in the straight-up polling question.”

When asked in the Pan American SMS survey to describe their position on same-sex marriage, 47.3 percent of respondents said they support both same-sex marriage and civil unions; 24.3 percent said they oppose same-sex marriage but support civil unions; 16.5 percent registered opposition to both same-sex marriage and civil unions; and 7 percent answered that they “oppose same-sex marriage for my church but not for others.” Five percent of those polled said they were undecided or declined to answer.

The analysis noted that 4 percent of the polling sample said they opposed same-sex marriage, then replied yes to the question about whether the state should be allowed to issue marriage licenses to same-sex couples. An additional 4.25 percent of the polling sample indicated that they would vote yes to the referendum question after saying that they “oppose same-sex marriage for their church but not for others.”

“This suggests a much closer race on this issue than straight-up polling by several polling firms indicates,” the analysis concluded.

“We asked that first question because we’ve seen consistent differences between the actual result and what people tell pollsters on gay marriage questions in Maine and nationally,” Murphy said Wednesday.

Describing a phenomenon that pollsters call “social desirability bias,” Murphy said, “People give an answer that may not in fact indicate what they plan to do because they don’t want to appear biased.”

He noted that responses to the question on personal attitudes toward same-sex marriage reflect a nearly even split between those who support legalization and those who express reservations about it in one form or another.

“We looked at how those people in those segments said they planned to vote. That group’s a little harder to judge,” Murphy said. “If you take that first 4 percent and just half of that second group, you’ve got 6 percent of the total sample, it gets you down to 50 percent for support. My contention is that this is an awful lot closer than people are telling us. I think we saw this in 2009. All the polling, including our own, was wrong.”

Two other polls released last month place support for same-sex marriage ahead by single-digit margins. A Maine People’s Resource Center poll of 856 registered Maine voters Sept. 15-17 reflected support for Question 1 at 53 percent, with opposition at 43 percent and 4 percent undecided. A mid-September Public Policy Polling survey of 804 likely Maine voters placed the level of support for Question 1 at 52 percent, with 44 percent opposed and 4 percent undecided.

In 2009, pre-election polling generally showed support for same-sex marriage after petitioners collected enough signatures to place on the ballot a people’s veto of the Legislature’s approval of a law legalizing same-sex marriage. But when ballots were tallied, voters repealed the law 53 percent to 47 percent.

“Every independent poll in Maine so far this election cycle has shown that the freedom to marry has majority support,” said David Farmer, a spokesman for Mainers United for Marriage. “The latest poll has numbers consistent with other polling, showing between 58 percent support to 52 percent support.”

Farmer said the Pan American SMS Omnibus Poll’s preliminary question did not offer a clear response for those who support gay marriage, but not civil unions.

“The poll asks if people support ‘both same-sex marriage and civil unions,’” he said.”There was no option to say you support just marriage. Many of the strongest supporters of marriage do not support civil unions because they fall short of providing the same protections and security that civil marriage provides. The lack of a clear answer for strong supporters likely influenced the answers of strong supporters.”

Question 1 appears on this year’s state ballot as a result of a petition drive by supporters of same-sex marriage to let Maine voters revisit the issue at the polls. Again this year, most pre-election polls have shown support for the measure.

Pan American SMS, which conducted the survey from Sept. 24 to 28, listed the margin of error at plus or minus 4.9 percent. The survey showed greater support for Question 1 in Maine’s 1st Congressional District — with 63.6 percent in favor vs. 32 percent opposed — than in the 2nd District, where 48.3 percent of poll respondents said they would vote yes and 45.3 percent said they would vote no.

In other news related to Question 1, former National Football League Commissioner Paul Tagliabue and his family announced Wednesday that they had donated $50,000 to Mainers United for Marriage, the group leading the campaign to pass Question 1.

The family owns property near Boothbay Harbor and has spent summers in Maine for decades, according to the release.

“My family cares about Maine and about the freedom to marry,” Tagliabue said in a release. “We felt we had to get off the sidelines and get involved in this important campaign in a state that we love. Last winter, I spoke at Bowdoin College and met many young people disturbed by the fact that their lesbian and gay peers struggle for acceptance. This fight for marriage equality is something we feel passionately about not just for our son and his partner, who has been a part of our family for 20 years, but for all loving, committed couples.”

The release stated that Mainers United for Marriage has raised more than $3.4 million to advocate for passage of Question 1.