Senate Republicans yesterday weighed a proposal to scale back their constitutional amendment to ban same-sex marriages in hopes of picking up some votes, although they conceded that passage is still beyond their reach.

Democrats objected to the move and derided it as a desperation effort to avoid the embarrassment of a huge defeat when the Senate votes on the issue tomorrow.

The maneuvering came as the Senate entered its second day of debate on the amendment. Senate offices were deluged with phone calls and e-mails prompted by heavy grass-roots mobilizations over the weekend, topped off by two appeals for passage by President Bush.

Faced with the likelihood of falling far short of the two-thirds majority needed to amend the Constitution, some Senate Republicans were pushing for a chance to vote on an alternative that stated simply that marriage exists only between a man and a woman.

As currently drafted, the amendment consists of two sentences: "Marriage in the United States shall consist only of the union of a man and a woman. Neither this Constitution, nor the constitution of any state, shall be construed to require that marriage or the legal incidents thereof be conferred upon any union other than the union of a man and a woman."

Some Republicans argued that proposed language on other legal arrangements, such as civil unions, was confusing and could be interpreted as either sanctioning or banning such unions.

According to a GOP leadership aide, the Senate would vote first on the two-sentence amendment and then on an alternative limited to the first sentence. But Democrats, who earlier agreed to drop procedural objections and allow an up-or-down vote on the amendment itself, objected to the Republicans' new strategy and threatened to renew their procedural objections.

During debate yesterday, Republican Conference Chairman Rick Santorum (Pa.) said the amendment is aimed at protecting marriage and the family, not denying anyone's rights. He said the amendment was needed to "stop what I believe is the death knell of our society."

Sen. Dianne Feinstein (D-Calif.) described the debate as a "waste of time" in light of the likely outcome and said she believes Republicans are trying to "drive a division into the voters of America . . . one more wedge issue at a very difficult time to be used politically in elections." The issue should be left to states, she added.

Over the weekend, both sides engaged in frenetic efforts to stir up the grass roots.

Amendment supporters sought to mobilize conservative Christians in a Sunday satellite television broadcast from Memphis. They said the broadcast, called "The Battle for Marriage: Imminent Vote," reached more than a million viewers and was carried on hundreds of Christian radio stations.

The speakers, including the Rev. Chuck Colson and psychologist James Dobson, listed the office telephone numbers of 25 senators who were targeted as potential swing votes and urged viewers to deluge them with calls this week. "We know it had an effect. If you tried to call into the Senate today, you probably could not get through," Tony Perkins, president of the Washington-based Family Research Council, said yesterday.

The Family Research Council and other conservative Christian groups said they had collected 1.1 million new signatures on a petition for preserving "traditional marriage," on top of 1.4 million signatures they delivered to Congress on Friday.

On the other side, the Internet-based liberal group began a television ad campaign suggesting Bush is using the marriage issue to try to turn voters' attention away from the war in Iraq and the economy. A spokesman for the group said it had spent $147,000 to run the spots on CNN nationally and on cable channels in Washington and New York.

Senate Majority Leader Bill Frist (R-Tenn.) speaks at a news conference with the Alliance for Marriage, which backs the amendment to ban same-sex marriage. Alliance President Matt Daniels is at right.