The entire Democratic presidential field supports changing the president's policy -- something that can be done automatically via an executive order in the next presidential administration.
While many prominent social conservatives are adamantly opposed to any research that involves the destruction of human embryos, two of the leading Republican candidates for president -- Sen. John McCain, R-Ariz., and former New York Mayor Rudolph Giuliani -- have come out in support of reversing the president's ban on new embryonic stem cell research.
McCain holds that position even though he is perhaps the strongest opponent of abortion rights among the leading Republican candidates for president.
"This is a tough issue for those of us in the pro-life community," McCain said last month at a Republican debate at the Ronald Reagan Presidential Library. "I would remind you that these stem cells are either going to be discarded or perpetually frozen."
Another major candidate, former Massachusetts Gov. Mitt Romney once supported a version of the bill being vetoed Wednesday, but now opposes it. He believes that embryonic stem cell research should be legal -- though not supported by federal funds -- and is a strong supporter of the sort of alternate research methods the president is endorsing.
"I have a deep concern about curing disease," Romney said at the debate, with Schwarzenegger and fellow stem cell supporter Nancy Reagan sitting in the front row.
The latest ABC News/Washington Post poll found that 68 percent of the American people back stem cell research. While there's a definite political split -- more than three-quarters of liberals and moderates back the research, compared with 47 percent of conservatives -- the issue has moved far enough into the mainstream that all candidates must confront it.
"Stem cell research has overwhelming support with the American public," said Karlyn Bowman, a senior fellow at the American Enterprise Institute in Washington. "So candidates need to be able to talk about this issue."
ABC's Teddy Davis contributed to this report.