To override Bush's veto, they need to convince about 15 more House Republicans to vote for reauthorization of the Children's Health Insurance Program, known as CHIP.
"The president is wrong and Congress is right," said Montana Democratic Sen. Max Baucus. "The Congress is right to fight like hell to override this veto."
The House is expected to take the veto override vote on Oct. 17. The Senate, which has enough support to overturn the veto, won't act until the House vote.
Bush has only used the veto - his ultimate weapon - just three times before. And more times than not, Sen. Orrin Hatch, R-Utah, has stood against the president.
Hatch agreed with Bush when he vetoed a bill that would have led to a pullout of Iraq. But the Utah Republican opposed the president when he twice vetoed a bill that would have expanded stem-cell research.
Hatch is also one of the biggest backers of CHIP, having been a lead sponsor when it was first created a decade ago. He has repeatedly attempted to knock down the president's objections saying the president has been given bad advice and has misconstrued what the bill actually does.
On Wednesday, Hatch went even further, calling CHIP "the morally right thing to do."
"I hope that we can muster enough votes to overturn this veto," he said, promising to personally try to persuade some House Republicans. Groups such as the AARP, YMCA and children advocacy organizations throughout the country will also be working the issue.
Senate Majority Leader Harry Reid, D-Nev., said those voting against CHIP should reconsider or face political consequences, particularly in the House, where every member is up for re-election next year.
CHIP is a popular program that provides health insurance to children in families that earn too much to qualify for Medicaid but are too poor to buy private coverage. The program is run independently by each state with a mix of state and federal dollars.
Currently, 6.6 million children are receiving coverage. Congress overwhelmingly passed an extension that would bump the spending from $25 billion to $60 billion over the next five years, with the hope of covering a total of 10 million children. The new money would come from a large tobacco tax increase, tacking 61 cents onto the cost of a pack of cigarettes.
CHIP was set to expire Sept. 30, but Congress and the president agreed to extend it to mid-November.
Hatch and Rep. Jim Matheson, D-Utah, voted for the expansion, which is also supported by Utah Gov. Jon Huntsman Jr. The governor called the veto "ill-advised."
Sen. Bob Bennett and Reps. Chris Cannon and Rob Bishop, all Republicans from Utah, voted against the bill.
Matheson called the veto "shameful," while Cannon defended it by saying it is "a budget buster."
That is one of Bush's biggest complaints. He was pushing for a total of $30 billion for CHIP, not the $60 billion approved in the bill.
Hatch said Bush's proposal wouldn't even cover the children now in the program.
"And when I compare $60 billion to the trillions of dollars our government spends on health care, I believe it is a worthwhile benefit," Hatch said last week.
The president also claims the CHIP reauthorization is an attempt to "federalize health care."
Hatch called such a claim "political," since CHIP is not a Washington-run program. The federal government provides money to the states, which create and run the program.
Bush also complains about "crowd out."
"Our goal should be to move children who have no health insurance to private coverage, not to move children who already have private health insurance to government coverage," he said in announcing the veto.
Hatch said crowd-out was inevitable, but Bush overstates it. Even under the expansion a little more than 90 percent of the children involved will be in families making less than twice the poverty level.
* THOMAS BURR contributed to this article.
* More than 6 million kids participated in CHIP in '06. The bill Bush vetoed would have added 4 million more.
* Most states cap eligibility to families earning $41,228 a year for a family of four. The bill would have made it $61,842.