WASHINGTON  — Senate Democrats who back gay marriage have decided now is the time to repeal a federal law defining marriage as the union of a man and a woman.

The Democrats may satisfy their gay marriage supporters, but the bill won’t get very far.

The repeal could be approved by the Senate Judiciary Committee on Thursday, but the next stop — the full Senate — could be a long way off. The bill’s chief sponsor, Sen. Dianne Feinstein, D-Calif., says she doesn’t have the votes for Senate passage, and the bill would have no chance in a House controlled by Republican conservatives.

The chairman of the Judiciary Committee, Sen. Patrick Leahy, D-Vt., defended the timing of the panel’s likely vote on the Defense of Marriage Act. “It is never the wrong time to right an injustice,” he said.

Feinstein’s bill has 31 Senate sponsors, all Democrats. Most Republicans fiercely oppose the repeal.

“Traditional marriage between a man and a woman has been the foundation of our society for 6,000 years,” said Sen. Charles Grassley, R-Iowa, the ranking Republican on the Judiciary panel. “The Defense of Marriage Act protects this sacred institution, which I believe in, and attempts to dismantle this law are likely to be met with a great deal of resistance.”

Lacking enough votes in the House or Senate, Grassley said the Democratic effort in the Judiciary Committee “makes it no more than a cynical political gesture to the Democrats’ base.”

It is likely that the issue will be debated right up to the 2012 elections, while challenges to the law take place in several federal appeals courts. Conservatives vowed to make it a front-burner issue after President Barack Obama decided in February his administration no longer would defend the law.

Much has changed since President Bill Clinton signed the Defense of Marriage Act in 1996. The District of Columbia and six states now recognize gay marriage: Massachusetts, Connecticut, Iowa, Vermont, Maine and New Hampshire.

The federal law has a huge negative economic impact on all gay couples through the denial of federal government benefits.

The couples cannot file joint federal income tax returns and take deductions available in traditional marriages. There are no spousal Social Security benefits. They can’t take advantage of the Family and Medical Leave law that protects one’s job and health insurance during emergency absences. Surviving gay spouses have no protection from estate taxes.

Leahy voted for the law in 1996 but has since changed his mind.

“I voted for DOMA as a way to allow states to maintain their independence and define marriage as each state saw fit,” Leahy said.

Leahy said he now believes the law undermines protections in the states that allow gay marriage. He said the law “created a tier of second-class families who are not treated equally under the law.”

The repeal would not obligate any person, state or locality to perform same-sex marriages.

Feinstein, who voted against the current law, said, “It has been firmly established over decades that marriage is a legal preserve of the states.

“DOMA was wrong when it was passed and should be repealed. And this bill will do that. It will strike DOMA from federal law and restore the role of states in determining who may marry in this country. I believe the time has come.”

Obama said recently he is “still working” on his views of gay marriage. He supports civil unions but has thus far not backed same-sex marriage.

Numerous recent polls suggest a slight majority of Americans favor giving same-sex couples the right to marry.

Thirty-seven states currently have statutory Defense of Marriage acts. Three of those states have laws that predate the federal act.