Michigan Senate Democrats on Wednesday introduced two bills related to gay marriage, including one which seeks to repeal the state's ban on such unions.

One bill would allow the state to recognize the out-of-state legal marriages of gay and lesbian couples. Currently, gay couples can marry in 12 U.S. states and 14 nations, including Canada, Michigan's northern neighbor.

Another measure seeks to amend the Michigan Constitution to remove a 2004 voter-approved amendment which defines marriage as a heterosexual union.

Both measures, however, face an uphill climb in the Republican-led House and Senate.

The bills are sponsored by Minority Leader Gretchen Whitmer and Democratic Senators Rebekah Warren, Bert Johnson and Virgil Smith.

A poll released earlier this month and another published in November show a majority of Michigan voters support legalizing gay nuptials.

The latest poll shows 57 percent in favor and 37 percent opposed.

Earlier this month, lawmakers in Nevada gave an initial nod to a similar proposal. Grassroots efforts in Oregon and Ohio aim to put the question before voters.

(Related: Oregon gay marriage push begins.)