On the morning of Sept. 3, the first day the Pentagon said they could, Alicia Butler and her wife, Judith Chedville, who is a Texas Army National Guard officer, went to Austin’s Camp Mabry so Ms. Butler could get a military spouse identification card and register for the same federal marriage benefits provided to wives and husbands of heterosexual service members.

The two women handed a sheaf of official papers, including their 2008 California marriage license, to a clerk who glanced at the documents and declared, “It’s one of those.” She then called over her boss, who told the couple that they would have to travel to a federal military base like Fort Hood, 70 miles to the north, to get the ID, Ms. Butler recalled.

The reason: Texas is one of six states refusing to comply with Defense Secretary Chuck Hagel’s order that gay spouses of National Guard members be given the same federal marriage benefits as heterosexual spouses. Mr. Hagel’s decree, which applies to all branches of the military, followed the Supreme Court’s ruling in June that struck down part of the Defense of Marriage Act that had prohibited the federal government from recognizing same-sex marriages.

While a majority of states ban same-sex marriages, most are not fighting the new policy. But Pentagon officials say that in addition to Texas, Georgia, Louisiana, Mississippi, Oklahoma and West Virginia have balked. Each has cited a conflict with state laws that do not recognize same-sex marriages. (A West Virginia official said, however, that the state intended to follow the directive.) While the president has the power to call National Guard units into federal service — and nearly all Guard funding comes from the federal government — the states say the units are state agencies that must abide by state laws.