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Senator Bernie Sanders, fresh off a painful loss in New York, is facing a steep climb in the Pennsylvania primary next week, according to a new poll that shows him losing to Hillary Clinton by double digits.

A Monmouth University survey released on Wednesday found that 52 percent of likely Democratic voters in Pennsylvania support Mrs. Clinton while 39 percent back Mr. Sanders. As has been the case in many states across the country, Mrs. Clinton performs best with women and older voters, while Mr. Sanders is most popular with young men.

The deficit in Pennsylvania is problematic for Mr. Sanders, who needs to win the coming state voting contests by big margins if he hopes to chip away at Mrs. Clinton’s growing delegate lead. Four states, in addition to Pennsylvania, have primary contests next Tuesday.

“After her win in New York this week, these numbers in nearby Pennsylvania suggest that the entire Northeast is looking pretty good for the Clinton campaign,” said Patrick Murray, director of the Monmouth University Polling Institute.

Mr. Sanders returned to Vermont on Wednesday and said he was taking a day off the campaign trail to recharge himself for the next phase of the race. Two of his top advisers appeared to be divided in interviews after the loss in New York as to whether Mr. Sanders would fight for the nomination at the convention even if he is trailing in delegates.

In a fund-raising pitch on Wednesday morning, Mr. Sanders made clear that he has no intention of going away quietly.

“We still have a path to the nomination, and our plan is to win the pledged delegates in this primary,” Mr. Sanders said. “I am going to keep fighting for every vote, for every delegate, because each is a statement of support for the values we share.”

But after recent weeks in which the Democratic race grew increasingly contentious and personal, Mr. Sanders could soon face calls to consider dropping out or, at the very least, ease his attacks on Mrs. Clinton.

Debbie Wasserman Schultz, chairwoman of the Democratic National Committee, acknowledged on Wednesday that the nominating contest had become more tense recently. While she did not say that it was time for Mr. Sanders to quit, she expressed hope in an interview with Fox News that the tenor would be more civil.

“What I’m hopeful that they continue to do is to make sure that we stick to the issues and that we continue to lay out for Americans why it’s so important that we elect one of these two candidates as the 45th president of the United States,” she said. “And not get any more intense or divisive.”