WASHINGTON —Gay rights groups expect that a proposed constitutional amendment to ban same-sex marriage will come up for a vote in the U.S. House on Sept. 30, leaving lawmakers time to stake a position before November elections. The move could finally put an end to more than a year of back-and-forth from House committee rooms to chambers regarding the contentious amendment’s future, marked by sharp protests, cancelled hearings, cancelled votes, bizarre alliances and a campaign outing Congressional staffers. But if defeated, the amendment would certainly make an appearance in the campaign platforms of many conservatives and most likely on the...