ST. PAUL — When it comes to legalizing gay marriage in Minnesota, supporters have the appearance of momentum: voters rejected a constitutional ban last fall, public opinion shows growing approval and each day seems to bring another national politician flocking to their cause.

But underneath those favorable signs, they also have a math problem.

It’s a problem most potent in the Minnesota House. So far, not a single Republican has pledged support. If the Democratic majority is forced to pass it alone, only five members out of 73 could defect. And yet 17 House Democrats represent districts where a majority of voters wanted the gay marriage ban.

A “yes” vote from those members could make them politically vulnerable when they’re up for re-election.

“It’s a delicate situation,” said Rep. Tim Faust, DFL-Hinckley, whose largely rural, east-central Minnesota district backed the gay marriage ban amendment by 60 percent. And Faust said he thinks that understates the opposition to gay marriage among his constituents: “I’ve heard from plenty of people who told me they don’t want gay marriage but didn’t think that belonged in the constitution.”

Faust, like many of the House Democrats in the same circumstances, said he hasn’t decided how he’ll vote. Nationally, prominent Democrats — and even a growing number of Republicans — are now on board for gay marriage as support seems to gain momentum by the day. Just Friday, freshmen Democratic Sens. Heidi Heitkamp of North Dakota and Joe Donnelly of Indiana came out in favor.

But Heitkamp and Donnelly won’t face voters again until 2018. Minnesota House members are back on the ballot in 19 months.

All sides agree the House is the chamber to watch. Gay marriage has already survived a procedural vote in the full state Senate, suggesting enough votes to pass there, and Senate Majority Leader Tom Bakk has said it’s on hold pending House passage.

Richard Carlbom, leader of the pro-gay marriage group Minnesotans United, said his group is “a handful of votes short” in the House but is confident of nailing down the needed support.

He said too much is being made of the number of Democrats from districts that supported last fall’s proposed ban.

“This is a deeper question that requires more reflection,” Carlbom said. “Nobody should rely on what the vote was in November. They should think about how they themselves want to be perceived on this vote, and what they think is right.”

Democrats say they’re being heavily lobbied.

Both pro- and anti-gay marriage groups have put a premium on activating their supporters in districts with legislators who are potential swing votes. Lawmakers say they’re getting regular phone calls, e-mails and office visits, and people on both sides are frequently showing up at town hall meetings in their districts.

Some House Democrats admitted their decision could come down to a choice between their own views and what looks like the will of their constituents. Freshman Rep. Joe Radinovich, DFL-Crosby, represents a central Minnesota district where 62 percent of voters backed the marriage amendment. But the 26-year-old lawmaker said he thinks people his age mostly support gay marriage, a sense confirmed by polls.

“I would say that people of my generation seem to have made up their mind on this question and I find myself thinking along those lines as well,” Radinovich said. But he’s not ready to commit to voting for the gay marriage bill.

“I am considering my views versus the views of my district,” Radinovich said. “It’s a tough thing and it’s weighed on me personally.”

Supporters of the gay marriage bill argue that lawmakers shouldn’t assume they will be punished by voters who oppose it.

They argue that many other issues, from local concerns to taxes and spending to national political currents, will be factors in how people vote in 2014 state House races. If the bill passes and gay marriage becomes legal this Aug. 1, voters will have had 15 months to get used to seeing gay couples wed by the next election.

Gay marriage “is one of those issues where voters understand that reasonable people can have a difference of opinion without necessarily having an impulse to punish them,” said Rep. Steve Simon, DFL-Hopkins, who supports the bill.

For every House Democrat whose district supported the amendment ban, there is a House Republican whose district rejected it — in fact, 21 House Republicans hail from districts where the amendment failed. But so far, only one Republican in the entire Legislature — Sen. Branden Petersen, R-Andover — has said he would vote to legalize gay marriage.

Simon said he believed “a Branden Petersen figure” in the House would help get the bill over the hump there.

“Even one Republican, one brave Republican who would be willing to vote for marriage equality would make a difference,” Simon said.

That prospect took a hit this week when four Republicans seen as possible votes for gay marriage introduced a bill to instead legalize civil unions. Gay marriage supporters said civil unions would leave gay relationships trapped in a second-class status, but those four Republicans all said civil unions were as far as they’d go and that they’d vote against gay marriage.

Democratic Rep. Kim Norton also signed on to the civil union bill. While Norton’s Rochester district defeated the amendment, she said many constituents told her they don’t support gay marriage — they just thought the issue didn’t belong in the constitution.

Norton said she hasn’t made up her mind how she’ll vote if the gay marriage bill reaches the House floor. Other swing House Democrats said the same.

“We are elected to come down here and vote for what we believe is right,” said Faust, of Hinckley. “And so my answer is that although I listen to everybody and I give everybody the opportunity on every issue to convince me that they are right, at the end of the day I have to push the button that I believe is right.”