WASHINGTON – Congress embarks this week on the weightiest of debates on morality and the march of science, deciding whether to use public money for embryonic stem cell research and, in turn, setting up President Bush’s first veto.

Neither the House nor Senate has demonstrated enough support for the bill to override a veto, though the House probably will try, just to give Mr. Bush a definitive victory in the showdown.

Supporters of the research hold out faint hope that Mr. Bush, presented with new data and pressured by election-year politics, might reverse course and sign the bill.

“This would be his first veto in six years, on something that the vast majority of the public supports,” said Senator Harkin, a Democrat of Iowa. “What would come down on him would be all the scientists, all the Nobel laureates and everyone else who supports it.”

Polls show that 70% of the public supports the bill, which would expand federal aid for embryonic stem cell research. The process is believed by many scientists to hold the most promise for curing diseases such as juvenile diabetes, Alzheimer’s, and Parkinson’s that strike millions of people.

The bill comes before the full Senate at the same time that Republicans, with their congressional majority at stake, are trying to energize their conservative base of voters during the fall elections.

Set for House action are bills to protect the Pledge of Allegiance from court challenges and a constitutional amendment to ban gay marriage, which failed in the Senate. Bills to encourage stem cell research from sources other than embryos also are expected to be voted on this week.

But it is the Senate’s stem cell bill that probably will draw the most attention – and Mr. Bush’s first veto.

In 2001, Mr. Bush halted federal funding of new embryonic stem cell studies, comparing them to abortion because the process of extracting the crucial stem cells destroys the days-old embryo.

He said at the time that such federal support for research could continue on the 78 stem cell lines then thought to exist. But in the years since, the National Institutes of Health have confirmed that a fraction of that number of lines exist and that few, if any, are viable for clinical trials.

Supporters hope that development might change Mr. Bush’s mind. But the White House, struggling for election-year credibility with its conservative base, has left no wiggle room in its public and private statements of opposition.

Several lawmakers who have spoken to Mr. Bush, adviser Karl Rove, and other White House officials in the year since the House passed the bill say they consistently have rejected any talk of compromise.

Mr. Rove last week said Mr. Bush was “emphatic” about his intent to veto the bill. White House spokesman Ken Lisaius said Friday the president would follow through if the bill came to him.

That could happen this week. Vote counters on both sides of the debate in the Senate say at least 60 votes for the bill exist – perhaps as many as 64; that’s enough to pass it. But 67 votes would be required to overturn a veto if all 100 senators are present.

GOP Senator Lott, who said he will vote for the bill and predicted it will pass the Senate, said yesterday he believes “something could be worked out.”

“I think Congress has to go ahead and act, and then we’ll take it from there,” he told CNN’s “Late Edition.”

The House was 50 votes short of its two-thirds majority when it passed the bill last year, 238-194. House leaders were planning for a veto override attempt as soon as Mr. Bush vetoes it, probably before week’s end.

House sponsor Rep. Mike Castle, a Republican of Delaware, said he expects support for the bill to grow beyond last year’s tally, but would not venture whether enough will switch to override a veto.

“A number of (House) members have told me they regret voting against it last year,” Mr. Castle said.

Scientific advances, public support, and appeals for passage from former first lady Nancy Reagan have given the bill unprecedented momentum.

In numerous behind-the-scenes phone calls to lawmakers and a few public statements, President Reagan’s widow generated more votes throughout debate in both houses and inspired the majority leader, Senator Frist, a Republican of Tennessee, to break a standoff with conservatives who have blocked a vote.

She is expected to weigh in again this week with calls to senators and perhaps a statement, said several officials with knowledge of her plans.

Opponents of the bill are, like Mr. Bush, firm in their belief that destroying embryos for science is immoral. They say that adult stem cell research is closer to curing some diseases.

Senator Coburn, a Republican of Oklahoma, last week withdrew his objection the Senate debating the bill this week in response to an appeal from Dr. Frist and other senators. But he made clear he thinks the timing of the debate hurts Mr. Bush.

“I think politically it’s stupid to have this debate now,” Mr. Coburn said. “He will cast his first veto over this, which people will interpret as that he doesn’t care about the curing of chronic disease. Nothing could be further than the truth.”

Dr. Frist, who supports embryonic stem cell research, agreed to also hold votes on two other measures this week that Mr. Coburn and others can support.

One, sponsored by Senator Santorum, a Republican of Pennsylvania, would encourage the search for crucial all-purpose stem cells from sources other than embryos.The second, sponsored by Mr. Santorum and Senator Brownback, a Republican of Kansas, would prohibit the growing of fetuses for the sole purpose of harvesting tissue.

The House plans votes on those two bills later in the week.