(CNN) -- Sen. John McCain's campaign rebuked Sen. Joe Biden on Tuesday, saying the Democratic vice presidential nominee had "sunk to a new low" by raising a debate over who cares more for special needs children.

The Republican camp's sharp response came after Biden said GOP advocates for children with birth defects should support stem cell research.

During a campaign event in Columbia, Missouri, Biden did not mention his Republican counterpart by name but said, "I hear all this talk about how the Republicans are going to work in dealing with parents who have both the joy ... and the difficulty of raising a child who has a developmental disability, who were born with a birth defect."

Biden's support of stem cell research is at odds with the position taken by the Republicans' vice presidential nominee, Alaska Gov. Sarah Palin, whose 5-month-old son, Trig, has Down syndrome.

Palin, an evangelical Christian, opposes embryonic stem cell research because it involves the use of human embryos, but her running mate, GOP presidential nominee McCain, does support stem cell research involving embryos.

"Well, guess what, folks? If you care about it, why don't you support stem cell research?" asked Biden, the running mate of Democratic presidential nominee Sen. Barack Obama.

Those comments brought a sharp response.

"Barack Obama's running mate sunk to a new low today, launching an offensive debate over who cares more about special needs children," McCain-Palin spokesman Ben Porritt said. "Playing politics with this issue is disturbing and indicative of a desperate campaign."

Biden spokesman David Wade insisted that the Delaware senator's comments were not directed at Palin.

"This is a clash of policies, not a clash of personalities," Wade said. "We've heard not a dime's worth of difference between the McCain-Palin ticket and the Bush administration on medical breakthroughs that millions of parents and doctors believe could save lives and transform the quality of life for countless Americans."

During her acceptance speech at the Republican National Convention last week, Palin told parents of children with disabilities that she would be "a friend and advocate in the White House."

But the Alaska governor's support for the disabled has come under scrutiny since McCain chose Palin to be his running mate nearly two weeks ago.

Before her run for the vice presidency, advocacy for special needs programs had not been a central part of her political campaigns or during her administration, despite her sister's autistic son. Watch more on Palin's budget priorities »

Palin signed a bill this year increasing special needs funding but frustrated some of the bill's co-sponsors by stepping in only at the last minute.

Sonya Kerr, an Anchorage attorney specializing in disability rights, filed a lawsuit against the state and Palin, alleging that there are not enough services for kids with special needs, specifically a child with autism.

"I would say, welcome, Gov. Palin, to our reality and what we've been trying to deal with for a long time," Kerr said. "I hope that it means that there will be support on a bipartisan basis for what people with disabilities need so we are not a bargaining chip in the political process."

CNN's Deb Feyerick, Alexander Mooney and Rachel Streitfeld contributed to this report.

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