Updated

House Democratic leaders said Sunday they were working to gather votes to override a veto on a popular children's health program, but pledged to find a way to cover millions without insurance should their effort fail.

In talk show interviews, Speaker Nancy Pelosi and Majority Leader Steny Hoyer did not dispute claims by Republican leaders that the GOP will have enough votes to sustain President Bush's veto when the House holds its override vote on Thursday.

Pelosi and Hoyer promised to pass another bipartisan bill if needed.

"Isn't that sad for America's children?" said Pelosi, D-Calif., when asked about the GOP's assurances the override vote will fail. "It doesn't mean we aren't working hard throughout the country: governors, mayors, people who deal with children on a regular basis.

"We'll try very hard to override it. But one thing's for sure: We won't rest until those 10 million children have health care," she said in an interview broadcast Sunday.

Hoyer, D-Md., declined to predict Thursday's vote.

"This is a defining moment for the Republican Party, in my opinion," Hoyer said, before adding later: The program is "not going to die. We're going to go back and we're going to pass another bill."

House Democrats scheduled the vote after Bush earlier this month vetoed legislation that would increase spending for the State Children's Health Insurance Program by $35 billion over five years. Bush has called for a $5 billion increase.

An override requires a two-thirds majority in the House and Senate. The Senate approved the increase by a veto-proof margin, but the earlier House vote fell about two dozen votes short.

The program provides health insurance to children in families with incomes too great for Medicaid eligibility but not enough to afford private insurance. Bush has said the bill is too costly. The president now says he might be willing to provide more than $5 billion originally offered but that the current proposal shifts too much insurance burden onto the government rather than private providers.

On Sunday, House Minority Leader John Boehner, R-Ohio, said he hopes that Democrats will agree to negotiate once the veto is sustained so that the children's insurance program can be reauthorized.

"We will have the votes to sustain the president's veto," Boehner said. "And I think the differences are resolvable, but we're standing on our principle that poor kids ought to come first."

"Most people don't want government-run health insurance," he added. "Republicans are working on a plan that will provide access to all Americans to high-quality health insurance, make sure that we increase the quality of health insurance that we have in America."

Last week, Pelosi said Democrats were making some progress and hoped to "peel off about 14 votes" to override the veto. Republicans such as Sen. Charles Grassley of Iowa and Orrin Hatch of Utah also were working to sway wavering House GOP lawmakers.

On Sunday, Pelosi did not comment on the predicted vote tally.

"We'll take one step at a time. And, again, we'll maintain our bipartisanship and our fiscal soundness," she said. "And we'll talk to the president at the right time, when he makes an overture to do so, but not an overture that says, 'This is the only thing I'm going to sign."'

Pelosi spoke on ABC's "This Week," and Hoyer and Boehner appeared on "FOX News Sunday."