(Jan. 15) -- Some major conservative Christian groups said yesterday that they were pleased but not satisfied by a new White House initiative to promote marriage, and they stepped up pressure on President Bush to champion a constitutional amendment prohibiting same-sex marriage in his State of the Union speech next week.

"This is like lobbing a snowball at a forest fire," said Sandy Rios, president of Concerned Women of America, one of the largest conservative Christian advocacy groups. "This administration is dancing dangerously around the issue of homosexual marriage."

The conservative Christians' insistence on an amendment to prohibit same-sex marriage may put President Bush in a political bind as he starts his re-election campaign, caught between wooing potential swing voters and turning out his core evangelical supporters. Some conservative strategists warn that pushing to amend the Constitution to prohibit same-sex unions could turn off some potential Republican voters like suburban women, who might find excessive talk about the perils of same-sex marriage as intolerant, mean-spirited or weirdly obsessive.

"I think there are a lot of people that don't want to endorse a lifestyle contrary to their personal values, but they want to be tolerant," said Ed Goeas, a Republican pollster who is working with the Bush re-election campaign, "and quite frankly they don't like being put in a position where they look to be intolerant."

Mr. Goeas added: "The president hasn't been hesitant at all in saying he thinks marriage is between a man and a woman, period. Questioning whether you need a constitutional amendment is another matter. Those are major actions."

Mr. Bush's top political adviser, Karl Rove, citing polling data, has often said that he believed the failure of four million conservative Christian voters to turn out in the 2000 presidential election almost kept President Bush out of the White House. Projecting another close race this year, Mr. Rove has worked hard to stay in regular contact with conservative Christian political leaders.

A coalition of several prominent conservative Christian political advocates from organizations like the Family Research Council and the Southern Baptist Convention said it had been urging Mr. Rove and others in the White House to persuade the administration to embrace an amendment blocking same-sex marriage. Some, including Concerned Women of American and the Family Research Council, said they also hoped for an amendment to prohibit states from recognizing same-sex civil unions.

In his only public statement on same-sex marriage, President Bush left many evangelical leaders puzzled about his intention. In a television interview last month, Mr. Bush said he believed a marriage was "between a man and a woman" and that he would support a constitutional amendment "if necessary." But he also said that "whatever legal arrangements people want to make, they're allowed to make, so long as it's embraced by the state, or does start at the state level," and he emphasized the need for tolerance.

Ms. Rios of Concerned Women of America said Mr. Bush had implicitly endorsed gay unions. "It is the same as saying the federal government doesn't want to weigh in on slavery, but if the states want to call it chattel that is O.K.," Ms. Rios said.

Several prominent evangelicals said their concerns were not assuaged by a report that the White House was planning a $1.5 billion initiative to promote marriage.

Gary L. Bauer, who ran on a traditional-values platform in the Republican primaries in 2000 and is now president of the conservative group American Values, said, "If the White House puts this on the back burner or doesn't put political capital into it, that would deeply demoralize a large block of voters that they are expecting to turn out in November."

Several conservative Christians involved in the push for an amendment said they saw the State of the Union speech, when President Bush will lay out his agenda for the year, as a pivotal test. "Time is running out but the clock is still ticking," said Tony Perkins, president of the Family Research Council.

Christian conservatives say they are puzzled at the administration's hesitation because prohibiting same-sex marriage appeared broadly popular, at least in the months since the highest court in Massachusetts ruled that the state had to recognize gay marriages.

Opinion polls have shown more than 60 percent support the idea that marriage should be restricted to a man and a woman.

Other prominent conservatives, however, argue that yes-or-no polls do not show how significant an issue might be to a voter. "Because it is a new issue, we don't know how it is going to affect votes cast for candidates," said Grover G. Norquist, a conservative strategist and the chairman of Americans for Tax Reform.

Mr. Norquist said some potential Republican voters might be turned off by raising the issue to a constitutional level, just as they were by too much talk of guns or abortions. "Obsessions turn people off," he said.

There are also gay Republicans to consider. About a million of them, or a quarter of the 4 percent of voters who identify themselves as gay, turned out for President Bush in the last election, Mr. Norquist said, citing polls of those who had cast votes.

How Mr. Bush himself feels about the issue personally is also unclear. Mr. Bush has made no secret of his own born-again faith. But some gay Republicans say he appears far more friendly to gays than previous Republican administrations. The administration has invited leaders of two gay groups, the Log Cabin Republicans and the Republican Unity Coalition, to the White House.

One of President Bush's longtime friends from Texas, Charles Francis, now heads the Republican Unity Coalition. At his inauguration, he sat near Mary Cheney, daughter of Vice President Dick Cheney, and her female partner.

Ms. Cheney is now director of vice-presidential operations in the Bush-Cheney re-election campaign.

In a debate in the 2000 campaign, Mr. Cheney spoke sympathetically of same-sex civil unions. "It's really no one else's business in terms of trying to regulate or prohibit behavior in that regard," he said. Last week, however, Mr. Cheney told The Denver Post that he would back any decision President Bush made on the question of an amendment.