WASHINGTON — Legislation to rescue the Children’s Health Insurance Program sailed through a Senate committee on Wednesday, but touched off a partisan conflict in the House, diminishing hopes that the popular program would be quickly refinanced.

Funding for the program expired on Sunday, and state officials said they would soon start notifying families that children could lose coverage if Congress did not provide additional money. It was impossible to say when Congress might pass a bill and send it to President Trump.

By voice vote, the Senate Finance Committee approved a bill on Wednesday that would provide more than $100 billion over five years for the program, which insures nearly nine million children.

The committee chairman, Senator Orrin G. Hatch, Republican of Utah, hailed the bill as “a prime example of what government can accomplish when both parties work together.” Mr. Hatch wrote the bill with the senior Democrat on the committee, Ron Wyden of Oregon, just as Mr. Hatch helped create the program in 1997 with Senator Edward M. Kennedy, Democrat of Massachusetts.