The Senate approved a bipartisan children’s health insurance bill on Thursday, putting the political triumph of a veto override within Democrats’ reach as one senior Republican said he would help the majority round up votes for the plan.

The $35 billion expansion of the State Children’s Health Insurance Program (SCHIP) won over 18 Republican senators on an early motion to end debate, helping Democratic leaders rebound from weeks of struggle over Iraq.

Sen. Chuck Grassley (Iowa), one of two Republican negotiators of the final package, said he would help court House members for an override. About a dozen House Republicans would need to back the SCHIP bill to undo a veto, in addition to the 45 who joined Democrats for a surprisingly strong Tuesday vote.

“We’re going to try [to see] if we can convince people in the House to change their vote,” Grassley said, adding, “All I can do is make phone calls.”

Some GOP supporters have urged Democrats to give ground to the White House, which wants a $5 billion SCHIP expansion. But Grassley, the senior Republican on the Finance Committee who helped pass Bush’s tax cuts and Medicare drug bill, suggested sympathy for House Democrats who reluctantly bowed to Senate pressure and removed Medicare changes from their SCHIP bill.

“I think they’ve gone a long ways,” Grassley said. “I’m telling you to tell them not to negotiate anymore, and I shouldn’t have said that.”

Grassley has suggested that, were he a Democrat, he would send the SCHIP measure to Bush repeatedly until the president agreed to sign it. Finance Committee Chairman Max Baucus (Mont.) and other Democrats appear open to that tactic, which recalls liberal activists’ message to the majority on this spring’s war supplemental bill.

“I’m willing to consider any strategy that allows us to put as much pressure as possible [on Bush], because I think it warrants that,” Sen. Bob Casey Jr. (D-Pa.) said.

Senate Majority Leader Harry Reid (D-Nev.) said House Majority Leader Steny Hoyer (D-Md.) has told him “the votes are there to override a veto in the House.” But Reid acknowledged that forcing the SCHIP bill into law would be difficult, and Hoyer said later that he needs more time.

“I think we can [get the votes], but whether we’ll be able to or not is another question,” Hoyer told reporters. House Democrats estimate they would pick up another 10 votes as of now, he added.

A veto override would be an undeniable coup for Democrats. But whether an override succeeds, SCHIP is sure to become fodder for the 2008 campaign season. Liberal-leaning activist groups already have begun running ads against GOP opponents of the bill, seeking a win-win situation: If the veto holds, vulnerable Republicans will take a hit; if Bush is overridden, Democrats can claim victory.

“What it’s showing is, on the domestic agenda, Democrats have the strong upper hand and Republicans are beginning to break ranks,” said Sen. Charles Schumer (N.Y.), vice chairman of the Democratic Caucus. “This will happen on Iraq as well. It hasn’t happened yet.”

Senate Minority Whip Trent Lott (R-Miss.) and Rep. Joe Barton (R-Texas) have offered an 18-month extension of SCHIP at levels higher than the White House’s proposal. They charge Democrats with forcing a political showdown that jeopardizes continued funding for SCHIP, which expires Sunday.

Democrats have opted to extend SCHIP funds through the continuing resolution that keeps government spending at current levels until mid-November. That CR is expected to pass the Senate on Friday.

Manu Raju contributed to this report.