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Conservatives say any benefits derived from research on already dead embryos is morally wrong. Across the divide, many have criticised the very limited scope of research allowed under the president's funding plan.
"What we believe is that the scientific community should set the standards," said Peter Van Etten, president of the Juvenile Diabetes Research Foundation.
"We are very concerned whether this is sufficient to do the work that needs to be done."
"The trade-off he has announced is morally unacceptable," said its president, Bishop Joseph A Fiorenza.
"Federal government, for the first time in its history, will support research that relies on the destruction of some defenceless human beings for the possible benefit to others."
Republican House Majority Whip Tom DeLay felt the same way. "The technique used to create the stem cell lines did not respect the sanctity of life," he said in a statement.
'Limited'
Those willing to listen, however, offered qualified support. Many are relieved that at least some research on embryonic stem cells can go ahead.
"President Bush's decision means that important stem cell research will move forward, giving hope to millions of people suffering from debilitating diseases and injuries," said Bill Frist, a senator from Mr Bush's Republican Party and himself a former surgeon.
Democratic Senator Edward Kennedy said the decision was "an important step forward", but criticised the measure for not going far enough.
His was a view shared by Dr Diane Krause, a researcher at Yale University School of Medicine. "Well, at least they're allowing some federally funded work on human embryonic stem cells," she said.
"But it will be limited by its very nature of being a limited number of cell lines. What we can do with them will be limited."
But the fact that money will be forthcoming from taxpayers was welcomed in the scientific community.
"It was a very good, clear and balanced outcome," said Carl Feldbaum, president of the Biotechnology Industry Organization, which represents 1,000 biotech firms and 150 universities conducting stem cell research.
"The president's decision is a major step forward for patients."
Pro-lifers 'delighted'
Notably, the anti-abortion National Right to Life Committee was amongst those pleased at the limited nature of the research to be funded.
It said it was acceptable to benefit from already dead embryos - as long as no more were killed.
"We are delighted that President Bush's decision prevents the federal government from becoming a party to any further killing of human embryos for medical experimentation," said spokesman Laura Echevarria.
There was nothing the president could do to "restore the lives of those embryos who have already died", she said.