In the first and only veto of his presidency, Bush rejected a similar measure last year.
The debate is emotionally charged. Advocates call stem cell research the best hope for potential cures for ailments like Alzheimer's disease, diabetes and spinal cord injuries. But the testing requires destruction of days-old embryos, and opponents say it is immoral.
"The administration strongly opposes Senate passage of (the bill), which would use federal taxpayer dollars to support and encourage the destruction of human life for research," the White House said in a statement threatening a veto.
Iowa Democratic Senator Tom Harkin, a chief sponsor of the bill, countered: "It's time we provide hope to millions and expand stem cell research."
Democrats won control of the US Congress from Bush's Republicans in November promising to expand federal funding of stem cell research, which is now restricted by Bush to batches available as of August 2001.
White House spokeswoman Dana Perino said Bush stood firm.
"The president weighed this issue very carefully back in 2001 and has thought about it since. And he believes that clear moral line that he established back in August of 2001 is a good place for the country to be," Perino said.
Stem cells are a kind of master cell for the body, capable of growing into various tissue and cell types. Those taken from embryos are especially malleable. Scientists hope to use the cells to repair tissue damaged by disease or injury.
In the 100-member Senate, backers and foes debated the measure as they counted votes and tried to determine if supporters could get the two-thirds majority needed in both the House and the Senate to override a Bush veto.
"It's going to be very close," Harkin said.
Earlier this year, the House passed a similar stem cell bill on a vote of 253-174 - about three dozen votes short of a two-thirds majority.
Another bill being considered would not lift Bush's restrictions and critics said it was inadequate. But with the backing of the White House, the Senate seemed certain to pass it this week.
That measure would encourage stem cell research using embryos that have naturally lost the ability to develop into fetuses. It would also support the creation of a bank of stem cells taken from amniotic fluid and placentas - two recently discovered potential sources.
"We are offering an opportunity to move the ball forward," Republican Senator Norm Coleman of Minnesota said.
