Even if the House manages to pass the bill, the Senate would still need to give its approval in order to avert a shutdown early Saturday morning, and at least nine Democrats are needed to overcome an expected filibuster.
The six-year extension of CHIP funding is important for Democrats, who have strenuously complained that federal funding for the program was allowed to lapse last fall.
But Republicans have postured all week as the champions of CHIP, which began under President Bill Clinton.
“I feel that it makes no sense for Democrats to try and bring us to a shutdown, to try and cut off CHIP funding for the states that are running out of money, like Minnesota and Washington and Kentucky and other states,” Mr. Ryan said.
Senator Mitch McConnell of Kentucky, the majority leader, also highlighted the CHIP funding as he expressed hope that Democrats would support the stopgap bill.
“The Democrats in the Senate have been very consistent in clamoring for addressing the children’s health care program,” Mr. McConnell said on Wednesday. “This does it with a six-year reauthorization. They claim they don’t want to shut down the government, so it seems to me it would be a rather attractive package. I certainly hope that’s the way they look at it.”
But Democrats are under heavy pressure to oppose any spending bill that does not protect the young immigrants, known as Dreamers, who are now shielded from deportation from an Obama-era initiative that Mr. Trump rescinded. They charge that the Republicans are making children’s health care a bargaining chip to force them to drop their demands on immigration.
By calling on CHIP to be dropped from the stopgap spending bill, Mr. Trump effectively backed the Democrats, although he may not have intended to.
Why the president suddenly undercut Republican arguments was not immediately clear. On Wednesday, the Trump administration released an official statement endorsing the stopgap measure, including the extension of funding for CHIP.
Aside from the sudden debate over children’s health care, the fate stopgap measure still seemed uncertain because of resistance within the House Republican conference. Most House Democrats are expected to oppose the bill.