A proposal to legalize same-sex marriage breezed through a final House committee Monday night, setting the stage for a possible final floor vote later this week.

By a voice vote, the House Ways and Means Committee approved $688,000 to provide health insurance for same-sex spouses of state employees each year.The amount is partially offset by about $10,000 in fees the state expects to collect from gay and lesbian couples seeking marriage licenses.

The measure could come to the floor of the DFL-controlled House for a final vote later this week. The Senate is weighing a similar measure, which DFL Gov. Mark Dayton said he will sign.

“Thousands of families are headed by same-sex parents in our state, and they should not have to wait another day for the joys, opportunities and responsibilities that come with marriage,” said Richard Carlbom, campaign manager for Minnesotans United, which is pushing for legalization of same-sex marriage.

Some Republicans sound increasingly resigned to the notion that they don’t have the political muscle to block same-sex marriage from becoming law in Minnesota.

“Elections have consequences and voters decided to have the left wing of the DFL have all three branches,” said state Rep. Michael Beard, R-Shakopee. “Is it inevitable? I’d say probably. They can do pretty much anything they want to do.”

Rep. Mary Liz Holberg, the ranking Republican on the House Ways and Means Committee, said she doesn't know how the issue will ultimately play out.

“Is it inevitable? I don’t know," said Holberg, R-Lakeville. "I haven’t spent a lot of time thinking about it. It’s out of my hands. Around here, you focus your energies on things you can do something about.”

