"The president is emphatic about this," Karl Rove said.
Mr Bush is prepared to use his veto power for the first time should it prove necessary, although this "is something we would, frankly, like to avoid", he said.
The House of Representatives passed the bill last year and it moves to the Senate for consideration this month. Opinion polls have shown that increasing stem cell research is popular with voters who are swayed by the prospect, one day, of discovering cures for diabetes, Alzheimer's, Parkinson's disease and other life-threatening ailments.
In 2001 Mr Bush limited federal funding to research into 78 existing stem cell lines, prohibiting the use of federal money on research into new lines or stem cells culled from frozen embryos. Of those 78 initial lines, 22 remain viable for research purposes. The proposed legislation would allow for funds to be spent on stem cell research using embryos that would otherwise have been thrown out by fertility clinics.
"We were all an embryo at one point, and we ought to, as a society, be very careful about being callous about the wanton destruction of embryos, of life," said Mr Rove. The latest research, Mr Rove said, showed that "[we] have far more promise from adult stem cells than from embryonic stem cells."
The bill will become veto-proof if it attracts the support of 67 or more Senators, enough to override Mr Bush. Bill Frist, a former surgeon and the Republican Party's leader in the Senate, supports the bill.
The issue is becoming another front in the battle for victory in this November's mid-term elections. Democrats have targeted seven sitting Republic congressmen with advertisements criticising their record on stem cell issues, while ballot initiatives in states such as Wisconsin and Missouri seek to protect embryonic stem cell research. Other states, such as California, have already authorised the funding of additional stem cell research.
"I don't think we'll see government funding for this of any real sort, which means America may need to take it state by state. It's a sad way of doing big science but it may be the only way to get it done," says Christopher Thomas Scott, executive director of Stanford University's programme on stem cells and society.
Mr Bush's threat to veto the legislation combines personal conviction with political expediency. Mr Bush's own pro-life stance is rarely questioned but the pro-life movement has on occasion grumbled that his administration has failed to advance the movement's agenda as much or as quickly as might have been imagined.
However, with Republicans still trailing in the polls, policy pledges that can be relied upon to motivate the party's base are likely to prove irresistible to Mr Rove and his colleagues, who suspect that whichever party motivates its hardcore supporters more effectively will be victorious in November. Democrats need to win six Senate seats and pick up 15 seats in the house to regain control.