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Traditional-values groups are hoping Gov. Susana Martinez will step in.

Close to 2,000 emails have been sent to her to protest such lawlessness, said Christopher Plante, regional coordinator of the National Organization for Marriage.

Beginning with President Obama’s decision not to defend DOMA, “there’s this idea that with the marriage issue, it’s OK to defy the law, it’s OK to be a law unto yourself, it’s OK that if you’re in the executive branch, you’ll suddenly become part of the judicial branch and declare things unconstitutional,” Mr. Plante said. Now it’s “trickled down” to the clerks.

Mrs. Martinez, a Republican, said she thinks voters — not courts, politicians or “one random county clerk” — should decide issues regarding same-sex marriage.

Next month, court rulings are expected in Illinois and New Jersey that could pave the way to gay marriage. Such lawsuits also have been filed in Arkansas, Hawaii, Kentucky, Michigan, Nevada, North Carolina, Oklahoma, Utah and Virginia.

In the political arena, Hawaiian Gov. Neil Abercrombie, a Democrat, may call a special legislative session to permit lawmakers to enact gay marriage. In Oregon, gay-rights activists are collecting signatures to repeal a voter-passed constitutional amendment that permits marriage only between a man and a women. Gay-rights groups in Florida and South Carolina are planning campaigns against similar state amendments.

In Indiana, where lawmakers have a year to decide whether to let voters speak on gay marriage, a group called Freedom Indiana recently said it would call for them to abandon that course.

This article is based in part on wire service reports.