Updated

President Bush on Wednesday vetoed a five-year, $35 billion expansion of the current State Children's Health Insurance Program, arguing the new program offers government-run health care to too many Americans who don't need it.

Democrats are confident they have a winning issue and are working hard to find enough votes in the House to override the veto. The Senate already has enough votes to override.

"Today the president showed the nation his true priorities: $700 billion for a war in Iraq, but no health care for low-income kids; $50 billion in subsidies for huge oil companies; but no health care for low-income kids; $8 billion lost to waste, fraud, abuse, and no-bid contracts in Iraq, but no health care for low-income kids," said Rep. Rahm Emanuel, D-Ill.

"Millions of American children and their families won't forget that they are on the bottom of the president's priority list," Emanuel said.

"Once again, the Democratic Party are aligned with 70 percent of the public," House Majority Leader Steny Hoyer, D-Md., said Tuesday.

On Wednesday, Hoyer announced Oct. 18 as the date the House will attempt to override the veto. He is looking for about 15 Republicans to switch their votes but said he has gotten no commitments so far.

The veto — the fourth of Bush's presidency — took place without fanfare, though the president addressed the matter while in Lancaster, Pa., where he gave remarks on the budget and spending.

"I just vetoed a bill today, and I want to explain to you why. It's called SCHIP, children's health insurance policy," Bush told the Lancaster Chamber of Commerce and Industry. "The intent of the program was to focus on poorer children, not adults or families earning up to $83,000 a year. It is estimated that if this program were to become law, one out of every three person(s) that would subscribe to the new expanded SCHIP would leave private insurance. The policies of the government ought to be to help poor children and to focus on poor children."

The president has said that the 61-cent tax on each pack of cigarettes to pay for the measure is regressive, and the government should not be providing health care to families whose income is as much as $80,000 a year. He also expressed concern that the offer of low-cost, government-provided health care will encourage many people who already are covered by private insurance to switch, adding considerable strain to the government system.

White House spokeswoman Dana Perino said Wednesday that Congress sent the bill to the president knowing that he wouldn't sign it, and it's now up to lawmakers to come up with an alternative. Bush had requested $5 billion more for the program over five years.

House Minority Whip Roy Blunt said he was "absolutely confident" that the veto will be sustained. Perino said Congress must negotiate a bill that will ensure that children in families that make less than 200 percent of the poverty level are taken care of before the program is expanded beyond them.

"The president is willing to look at ideas" for a compromise "with the focus on the original intent that the neediest children are taken care of first," Perino said.

Under the vetoed plan, government-sponsored health coverage would have been expanded from 6.6 million people, mostly children, to include an additional 4 million kids and 700,000 adults. Currently, 9 percent, or 6 million, of the 43 million uninsured Americans are children under 18. SCHIP is available to people who earn too much to qualify for Medicaid, but are not able to afford private insurance.

Republicans who oppose the bill aren't going to get off easily. The Democratic Congressional Campaign Committee is already running ads against some GOP lawmakers who voted against SCHIP. Gerald McEntee, president of the American Federation of State, County and Municipal Employees union, said a coalition of liberal groups planned more than 200 events throughout the nation to highlight the issue.

FOX News' Major Garrett, Malini Bawa and The Associated Press contributed to this report.