WASHINGTON — As the Senate held a rare Sunday session, the Republican leader said a potential deal was “coming together” on the government shutdown but there was no guarantee it would end an impasse now stretching to 40 days.

There have been few signs of progress over the weekend that could be crucial in a funding fight that has disrupted flights nationwide, threatened food assistance for millions of Americans and left federal workers without pay. Top Republicans are working to present a legislative package that would reopen the government into January while also approving full-year funding for several parts of government. The necessary Democratic support for that effort was far from certain.

“A deal is coming together,” Senate Majority Leader John Thune, R-S.D., said as he walked in to

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