WASHINGTON - Since President Bush's veto sent an extension of the State Children's Health Insurance Program back to Congress, political jockeying over the bill has hit an even higher level.

Advocacy groups have begun running TV and radio ads, supporters of the bill are trying to rally enough votes to override the veto, and opponents have been trying to explain their objections.

The spotlight is on the House, which did not pass the measure by a veto-proof margin. All sides are gearing up for an attempted veto override scheduled for Oct. 18.

It seems unlikely that Democratic leaders will be able to persuade the two dozen or so lawmakers needed to reach a two-thirds majority to change their votes. But a huge lobbying campaign is under way.

In Wyoming, the Service Employees International Union will begin running TV ads early next week through Oct. 18 urging GOP Rep. Barbara Cubin to support an override. She did not vote on the House version of the SCHIP bill.

Senate Finance Committee Chairman Max Baucus, D-Mont., one of the authors of the bill, remains hopeful that enough votes can be rounded up in the House to override. The Senate passed the bill by a bipartisan, veto-proof majority.

"There's a lot of ballgame left," said Baucus spokesman Barrett Kaiser. "And Max is putting his shoulder to the wheel to get this veto overridden. He's come an awfully long way, and he's not about to give up now."

Democrats feel the issue will play well for them during next year's elections. Baucus, who is up for re-election, has been running TV ads criticizing Bush for his stance.

Likewise, Republicans worry that the issue will hurt them. A group of 18 Republican senators, including Sens. Mike Enzi and John Barrasso of Wyoming, introduced on Thursday night a bill called the Kids First Act that would increase SCHIP spending by about $15 billion - which is $10 billion more than Bush proposed but $20 billion less than the bill Congress approved.

"This bill would provide federal funding for children in need and require that the money actually be spent on children from families with lower incomes," Enzi said in a statement. "… I believe I have some colleagues on the other side of the aisle in both the Senate and the House who see how unproductive a political stalemate like this can be for them and for us, but more importantly how it could negatively impact the children. If we are willing to suspend the politicking, even briefly, then I believe we could bring the president in and get a bill to him he would sign."

But the new bill is almost identical to one soundly defeated in the Senate two months ago, except it omits some health savings account and small business provisions that were in the failed bill.

If the House fails to override the veto, a likely outcome, lawmakers would pass either a short-term or a one-year extension of the current program and begin working on a new deal.

Congress has already approved a temporary extension of the program to keep it running beyond its expiration date of Sept. 30.

The measure Bush vetoed would have raised SCHIP funding by $35 billion over five years, paid for largely by a 61-cent-a-pack tax increase on cigarettes. Bush wanted to increase spending by $5 billion and opposes the cigarette tax boost.

Bush, who has taken criticism for opposing a bill to provide health care for low-income children, slightly opened the door to compromise.

"If they need a little more money in the bill to help us meet the objective of getting help for poor children, I'm more than willing to sit down with the leaders and find a way to do so," Bush said in a speech Wednesday.

But Senate Democratic leaders reacted strongly against his comment. They said House leaders, who had passed a $50 billion extension of SCHIP, had already compromised as far as they could by agreeing to the smaller Senate version.

Senate Majority Leader Harry Reid, D-Nev., called Bush's words an "insult."

"You cannot wring another ounce of compromise out of this," Reid said. "The president, what he has done with his macho pen, is really hurt children. He thinks he can waltz in here with his secretary of Health and Human Services, and sweet talk us - he can't. This is a man who is out of touch with reality."

Republicans who oppose the bill that Congress approved say it would expand government-run health care, that it would push some children from private to public health insurance and that some parents would continue to be covered in some circumstances.

But supporters note that states often involve private companies in providing the coverage and that it was the Bush administration that granted waivers to some states to allow parents to be covered.

Lawmakers said the bill that Congress approved would add 3.3 million children to the program, bringing the total covered to 9.9 million.

The administration wants to limit coverage to households under 200 percent of the poverty line, or an annual income of about $34,000 for a family of three.

Baucus said the new measure would simply extend current law, which limits coverage to 200 percent of poverty. States that want to cover over 200 percent must apply for and be granted waivers by the administration. A lower federal match rate would apply over 300 percent of poverty. The vetoed bill also had a new policy that states covering over 300 percent must first meet target enrollment levels for children below 200 percent of poverty.

SCHIP is a federal-state program to help children whose families don't qualify for Medicaid but cannot afford private health insurance to get coverage. Any SCHIP funding increase would be on top of the $25 billion now available over five years.