WASHINGTON — The government shutdown stretched into its 40th day Sunday even as senators stayed in Washington for a grueling weekend session hoping to find an end to the funding fight that has disrupted flights nationwide, threatened food assistance for millions of Americans and left federal workers without pay.

The Senate has so far shown few signs of progress over a weekend that could be crucial for the shutdown fight. Republican leaders are hoping to hold votes on a new package of bills that would reopen the government into January while also approving full-year funding for several parts of government. But the necessary Democratic support for that effort was far from guaranteed.

“We’re only a handful of votes away” from passing a bill to reopen the government, Senate Majority Leader J

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