AUGUSTA — The contest surrounding a ballot measure asking voters if they favor legalizing same-sex marriage could be tightening, according to a new poll that’s the first to ask respondents the exact wording of the question they will see on the ballot in November.

In addition, the poll — conducted by the Portland-based Maine People’s Resource Center — shows incumbent U.S. Reps. Mike Michaud and Chellie Pingree with comfortable leads over the Republicans trying to unseat them.

The Maine People’s Resource Center on Thursday released a second round of polling data on the heels of results from two polls released Wednesday that showed Angus King’s lead shrinking in the campaign for Maine’s open U.S. Senate seat.

The Maine People’s Resource Center — which is affiliated with the left-leaning Maine People’s Alliance, a statewide advocacy group — surveyed 856 registered Maine voters Sept. 15-17; its survey carries a margin of error of 3.35 percent. The North Carolina firm Public Policy Polling is expected to release more of its Maine polling data later Thursday.

The Maine People’s Resource Center found 53 percent of voters saying they would vote “yes” on a ballot question asking, “Do you want to allow the State of Maine to issue marriage licenses to same-sex couples?” Forty-three percent of respondents said they planned to vote “no,” while 4 percent of voters were undecided.

The 53-43 edge for same-sex marriage supporters is a narrower one than previous polls, though the resource center’s survey is the first to ask voters the exact question they will see on the ballot in November.

Maine Secretary of State Charlie Summers, also the Republican candidate for Maine’s Senate seat, finalized that wording at the end of July. Polls taken in June, before the question’s wording was finalized, found greater levels of support for legalizing same-sex marriage.

A poll by the Portland firm Critical Insights conducted June 20-25 found a 57-35 edge for same-sex marriage supporters, and a survey conducted by the MassINC Polling Group for the Boston public radio station WBUR June 13-14 found 55 percent of voters supporting the same-sex marriage initiative, compared to 36 percent opposing it. The Critical Insights survey asked voters, “Do you want to allow same-sex couples to marry,” and the WBUR poll asked voters if they supported a law that would allow same-sex couples to marry and “protects religious freedom” by not requiring clergy to perform same-sex marriages.

In the congressional races, Michaud led his Second District challenger, Kevin Raye, 56-37, while Pingree led challenger Jon Courtney 60-32 in the state’s First Congressional District.

The Michaud-Raye results were virtually unchanged from the Maine People’s Resource Center’s April survey, which found 53 percent of second district voters backing Michaud to 37 percent for Raye.

Those results contrast the last public survey sizing up that contest, which has been seen as potentially competitive by national Republican groups. The Portland firm Critical Insights found a closer contest when it polled voters in June. At that point, Michaud was leading Raye 47-35.

If poll results continue to show the race decidedly in Michaud’s column, it could determine the extent to which outside groups invest in the contest.

The closer results in June helped attract some support for Raye from outside Republican groups. The National Republican Congressional Committee elevated Raye to “Young Gun” status after the June poll, a label the committee reserves for candidates it sees as promising. More recently, Raye received the endorsement of the National Federation of Independent Businesses. And both he and Michaud have taken to the airwaves with television ads recently.

In the First Congressional District, Pingree’s 60-32 edge over Courtney also has changed little since the Maine People’s Resource Center’s April survey, when Pingree led Courtney 61-28.

Courtney has struggled to gain traction in his challenge against Pingree. His fundraising during the second quarter of 2012 amounted to about a tenth of what Pingree collected. He had $19,000 in campaign cash on hand as of June 30.

He also won the Republican nomination for the First Congressional District by a razor-thin margin over political newcomer Patrick Calder, and he’s struggled to gain the attention of national Republican organizations like Raye has.

The Maine People’s Resource Center found job approval numbers for Gov. Paul LePage are virtually unchanged from the group’s last survey in April. The most recent poll found 39 percent of respondents approved of the Republican governor’s job performance, compared to 54 percent who didn’t approve. In April, 39 percent approved while 56 percent did not approve.