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Gov. Bob McDonnell said it would be “very disappointing and unacceptable” if anyone voted against Mr. Thorne-Begland because of his sexual orientation.

“I believe candidates for judicial vacancies must be considered solely on their merit, record, temperament, aptitude, skill and commitment to follow the law,” he said. “I have long made clear that discrimination on the basis of such factors as race, religion or sexual orientation is not acceptable in any judicial appointment process. In my consideration of judicial candidates I only consider the individual’s ability to do the job well.”

The debate comes as national Democrats and Republicans line up on either side of the tangential issues of same-sex marriage and civil unions.

President Obama publicly expressed his personal support for same-sex marriage last Wednesday after maintaining for some time that his views on the subject had been “evolving.” That announcement came a day after North Carolina voters approved a constitutional amendment banning same-sex marriages in the state.

Vice President Joseph R. Biden was widely credited with helping lay the groundwork for Mr. Obama by saying May 6 on NBC’s “Meet the Press” that he was “absolutely comfortable” with married people of the same sex receiving the same rights and liberties afforded to heterosexual couples.

Rep. James E. Clyburn, South Carolina Democrat, went even further on Monday when he threw his support behind same-sex marriage, adding that there should be a national policy on the matter.

Despite his personal support, Mr. Obama said it should still be left up to the states. Thirty states have voted to adopt constitutional amendments banning same-sex marriage. The president said Monday that while he does not believe the federal Defense of Marriage Act (DOMA) that defines marriage as a man and a woman is constitutional, he declined to say whether he would work with Democrats in Congress to repeal it.

Pundits have started to describe the issue as a “litmus test” for the 2016 Democratic nomination for president. Govs. Andrew Cuomo of New York and Martin O’Malley of Maryland, both among the leading contenders for the party’s nod in four years, successfully backed the legalization of same-sex marriages in their respective states this year.

Rhode Island Gov. Lincoln D. Chafee, a Democrat, issued an executive order Monday to recognize out-of-state same-sex marriages as legal.

Still, despite bipartisan support in the Colorado state legislature, a proposal to legalize same-sex unions was blocked by Republicans in the state House Monday.