House Republicans Toil for a Spending Strategy With a Shutdown Close at Hand

The discussion amounted to a concession that House Republicans’ preferred way of funding the government — through passing a dozen individual spending bills — was no longer feasible with a deadline less than two weeks away, and after they squandered three weeks fighting over who should be speaker after Mr. McCarthy’s ouster.

They are still hoping to pass as many spending bills as possible to put themselves in a stronger bargaining position for negotiations with the Senate. But Mr. Johnson has faced the same headwinds Mr. McCarthy did in passing the funding measures, with some politically vulnerable Republicans unwilling to support bills saddled with deep cuts and conservative policy riders.

“The bottom line is that we have a speaker who wants to get this done, who understands that we’re going to need a little bit more time,” said Representative Mario Diaz-Balart of Florida, a top appropriator. “And then the question is, what’s the best way?”

The idea of a staggered spending deal met a chilly response from members of both parties in the Senate, where attempts to find a spending compromise have largely stalled as lawmakers wait for House Republicans to put down a marker for what they are willing to support.

“It seems to me that you would just constantly be having programs and agencies stop and go, stop and go,” said Senator Susan Collins of Maine, the top Republican on the Appropriations Committee. “And so I think that would increase the difficulty.”

The fight over keeping the government open was running parallel to Congress’s consideration of the White House’s emergency funding request for Israel, Ukraine and other national security needs. The House last week passed a partisan bill to fund Israel that is dead on arrival in the Senate, but the Senate has yet to present a counterproposal.

At the same time, top Senate Republicans were digging in against advancing any aid to Israel and Ukraine that did not include significant immigration policy changes and money, even though Democrats led by Senator Chuck Schumer of New York, the majority leader, quickly dismissed their initial offer as unacceptable.

“Making Ukraine funding conditional on the hard-right border policies that can’t ever pass Congress is a huge mistake by our Republican colleagues,” Mr. Schumer said. “By tying Ukraine to border, Republicans are sadly making it harder — much harder — for us to help Ukraine in their fight against Putin.”

Senate Republicans’ stance was something of a change from a group that had been mainly supportive of maintaining aid for Ukraine.

“If I were him, I would not underestimate the level of resistance he will run into if the issue of the border isn’t addressed,” Senator John Thune of South Dakota, the No. 2 Republican, said of Mr. Schumer. “We are just not going to get members who are willing to vote for any kind of supplemental package that doesn’t include that.”