WASHINGTON — As the 35-day government shutdown ties for the longest in American history on Tuesday , senators predicted that the impasse could end this week.

“I’m pretty confident,” said Sen. Markwayne Mullin, R-Okla.

After weeks without any movement, bipartisan talks among rank-and-file members have been picking up, leading to the first public signs of optimism that the shutdown could soon end.

Mullin said that some Democrats had privately indicated last week that they were willing to vote for the short-term Republican spending bill that would reopen the government through Nov. 21. But, Mullin said, Senate Minority Leader Chuck Schumer, D-N.Y., had instructed them to wait until after Tuesday’s elections so they wouldn’t depress turnout from the liberal base that has been urging the

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