Each ultimately must unseat a Democratic incumbent, overcome brushes with hate and confront passionate divisions within the GOP about the way they live their lives. The Republican Party is trying to soften its tone on divisive social issues, but many religious conservatives see homosexuality as immoral.
Innis is married to a man, as is former state Sen. Richard Tisei, R-Mass., who is expected to run again for the northeastern Massachusetts congressional seat he narrowly lost in 2012 to Democratic Rep. John Tierney.
In San Diego, former Republican city councilman Carl DeMaio is challenging first-term Democratic Rep. Scott Peters.
"You can't focus on any of the nasty comments or attacks — not just from far right, also from far left," DeMaio says.
During his unsuccessful 2012 Republican mayoral campaign, DeMaio and his male partner of six years were booed as they walked hand in hand in San Diego's gay pride parade.
"Every once in a while we'll get some hate that is truly over the top — a truly venomous voice mail message. Every time we need a lift-me-up, we play it and chuckle," DeMaio says. "It's just a reminder that what we're fighting for matters."
He is fighting his own party, too.
The GOP's formal platform, as set in its 2012 national convention, declares that "marriage, the union of one man and one woman, must be upheld as the national standard."
Republican opposition to gay marriage has become less visible recently as the GOP works to improve its image and polling suggests that most Americans support same-sex marriage.
Prominent social conservatives such as former Pennsylvania Sen. Rick Santorum and Ralph Reed, former leader of the Christian Coalition, declined to be interviewed for this story.
As a senator in 2003, Santorum, a leading candidate in the 2012 presidential primary, compared homosexual acts to child molestation and bestiality.
Last month, U.S. Rep. Randy Forbes, R-Va., drew national attention for pressuring the House Republican campaign arm not to support openly gay candidates. That led House Speaker John Boehner, R-Ohio, to pledge public support for gay Republicans.
Boehner traveled to Massachusetts in 2012 to help raise money for Tisei, who notes that more than 70 members of Congress supported his last campaign.
Still, Tisei says the GOP must do more to change the perception that "we're the party that wants to deny people their rights and interfere with their personal lives."