Supporters of a major expansion of the federal program to provide health care coverage for uninsured children — including an additional 35,000 Minnesotans — have one week to persuade about 20 reluctant House members.

An attempt to override the veto by President Bush of the State Children’s Health Insurance Program funding, passed overwhelmingly by Congress, is scheduled for a House vote Oct. 18.

Both Democratic Sen. Amy Klobuchar and Republican Sen. Norm Coleman said they will support an override of Bush’s veto last week, but the real test won’t be in the Senate — where the proposed $35 billion increase in funding for SCHIP passed with more than two-thirds support.

“Now the key is to work on House members who can override this,” Klobuchar said.

Coleman, however, said he is doubtful supporters of the bill will get enough House Republicans to reverse their position to allow for an override and suggested it’s time to negotiate with the president.

“We’ve got to find some middle ground,” Coleman said. “... We should be working today on a sensible bipartisan compromise.”

Congressman Tim Walz, a Mankato Democrat, said he thinks a consensus position was already met when a House-Senate conference committee worked out the bill that ended up easily passing both houses of Congress before being struck down by Bush.

The House originally passed a bill calling for a $47 billion increase for SCHIP over five years, an amount that would have brought coverage to 5 million children who otherwise would be uninsured, according to a summary of the bill by the Kaiser Family Foundation. The original Senate bill would have done the same for 4 million children, spending $35 billion over five years.

Walz said House members already had moved a substantial amount and shouldn’t need to drop more children from the program to satisfy Bush, who said that congressional Democrats were spending too much and is proposing $5 billion in additional SCHIP expenditures.

“That’s how we go to this compromise bill,” Walz said. “We may have gone as far as we can go.”

Bush’s proposed 20 percent increase in the program would actually force some children off the program because health care costs are rising so rapidly, according to the Congressional Budget Office. An increase of $14 billion is required simply to maintain existing enrollment, the CBO analysts said.

But Walz said it makes sense to do more than simply maintain enrollment because insuring children, and allowing them to get health problems treated in a timely manner, is fiscally prudent.

“This is a good investment,” he said. “It saves us money in the long run.”

Klobuchar agreed.

“If kids don’t have any health care insurance, they have a doctor and that doctor is the emergency room,” Klobuchar said. “And that’s incredibly expensive.”