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By Amy Chozick & Alexander Burns, New York Times–

PHILADELPHIA — After months of trying to sideline an unexpectedly deft and well-financed liberal opponent, Hillary Clinton on Tuesday won a series of primaries that freed her to present herself as the de facto victor of the Democratic nominating fight and gave her the impetus to shift focus decisively toward the November election.

Now all but certain to clinch her party’s nomination, Mrs. Clinton will continue to face the criticism of her party rival, Senator Bernie Sanders of Vermont. But she is expected to move swiftly to claim an early advantage against the leading Republican candidate, Donald J. Trump. Her advisers and allies say she will spend the coming weeks honing her message for the general election, and stepping up fund-raising that has lagged in the face of Mr. Sanders’s challenge.

“With your help, we’re going to come back to Philadelphia for the Democratic National Convention with the most votes and the most pledged delegates,” Mrs. Clinton told a crowd of 1,300 here after she took the stage to “Eye of the Tiger.” “And we will unify our party to win this election and build an America where we can all rise together.”

After a landslide win in New York last week, Mrs. Clinton had already begun to treat Mr. Sanders as a greatly diminished threat, concentrating her fire on Mr. Trump and, to a lesser degree, Senator Ted Cruz of Texas. Her victories in Pennsylvania, Maryland, Connecticut and Delaware on Tuesday will only accelerate that shift.

In recent days, she has sharpened her pitch about the general election’s stakes, heading off Republican attacks on her record as secretary of state under President Obama and delivering a more forceful message about the economy and the need to create jobs and lift wages.

“Imagine a tomorrow where hard work is honored, families are supported, streets are safe and communities are strong, and where love trumps hate,” Mrs. Clinton said Tuesday night, drawing applause at her play on Mr. Trump’s name.

Mrs. Clinton is not expected to publicly pressure Mr. Sanders to quit the race. Clinton advisers say any efforts to muscle him out could backfire, angering his supporters and Mr. Sanders, both of which Mrs. Clinton praised Tuesday night “for challenging us to get unaccountable money out of our politics.”

But a “super PAC” supporting Mrs. Clinton’s candidacy, Priorities USA Action, may start running general election ads even before the nominating contest ends.

Guy Cecil, the group’s chief strategist, said the group might run ads against Mr. Trump or Mr. Cruz, “depending on how the Republican primary develops and whether they decide to launch attacks against Hillary.”

In coming weeks, Mrs. Clinton will campaign in states with looming primaries, but she will also recharge and spend time in New York plotting a general-election strategy with advisers.

“She needs to be smart and calculated and prepare herself for a tough general election, and knowing her, she will be,” said Thomas R. Nides, a friend and adviser who worked for Mrs. Clinton at the State Department.

After months of focus on the 2,383 delegates needed for the Democratic Party nomination, her campaign has begun to analyze the Electoral College, working out potential races against Mr. Trump and Mr. Cruz. And the campaign will begin polling in traditional battleground states like Ohio and Florida.

But it will also pore over data in traditionally Republican states like Arizona, North Carolina and Georgia that could be in play, particularly if Mr. Trump is the nominee, and focus on demographics beyond the Democratic primary electorate.

“Realistically, the most important part in all of this are white working-class women,” said Geoff Garin, a pollster and strategist on Mrs. Clinton’s 2008 campaign who is now advising Priorities, citing Mrs. Clinton’s emphasis on issues like equal pay for women and an increase in the minimum wage.

Senator Chris Murphy of Connecticut, who campaigned alongside Mrs. Clinton in his state, said she must focus on how best to connect to a broader electorate that is in what he called a “revolutionary mood,” alluding to how Mr. Sanders has energized supporters. “You are not going to win this general election by proposing incremental changes,” Mr. Murphy said, adding that he hoped Mrs. Clinton “doesn’t shy away from proposing some big ideas to try to reorder the country, to the benefit of those that are hurting.”

Mr. Sanders’s campaign vowed Tuesday to remain in the fight through the California primary on June 7, and perhaps until the party’s convention in July. As word of Mrs. Clinton’s victories rolled in on Tuesday night, he gave a defiant speech in West Virginia, predicting he would win the state when it votes May 10.

Mrs. Clinton, who doggedly remained in the 2008 primary contest against Barack Obama until June despite his insurmountable delegate lead and Democratic calls for her to bow out, has said she will not call on Mr. Sanders to withdraw, but she has bristled at the implication that he could overcome her big leads in both pledged delegates and the popular vote.

Mrs. Clinton’s aides and allies are pressuring Mr. Sanders to run on issues rather than continuing to attack Mrs. Clinton’s ties to Wall Street or her previous support for global trade deals — attacks that Republicans are likely to use in the fall.

“If he tones down the rhetoric and continues to fight, he’ll go out on a very high note with a lot of people, including me, thinking he did a great service to American democracy,” said Edward G. Rendell, a former Pennsylvania governor, who supports Mrs. Clinton. “But if he keeps it up, it could be brutal.”

Mr. Sanders, whose sole win on Tuesday came in Rhode Island, did not attack Mrs. Clinton directly in his remarks on Tuesday night, but argued insistently that he would be a superior general-election candidate. As voters went to the polls earlier in the day, the Sanders campaign sent out a fund-raising email with an image of Mrs. Clinton and her husband, Bill Clinton, at Mr. Trump’s 2005 wedding, and accused Clinton allies of being “traitors” in their treatment of Mr. Sanders.

Still, Tad Devine, a senior adviser to Mr. Sanders, on Tuesday said that the campaign would not mislead voters about his chances at winning the nomination.

“If we are sitting here and there’s no sort of mathematical way to do it, we will be upfront about that,” he said.

Democrats supporting Mrs. Clinton have pointed to Senators Harry Reid of Nevada, Elizabeth Warren of Massachusetts and Chuck Schumer of New York as potential peacemakers, should the Sanders campaign keep up its pointed attacks on Mrs. Clinton.

“I’m going to be optimistic and say it won’t be necessary, but all of us are friends with Bernie and we’d pick up the phone and talk to him at any time,” said Senator Claire McCaskill, a Democrat from Missouri who is supporting Mrs. Clinton.

But Mrs. Clinton would do well to begin “building bridges” to Mr. Sanders, said David Axelrod, a former senior strategist for the Obama campaign.

“It seems certain Bernie will run through the last primaries, which is inconvenient and costly,” he said. “Still, when you’re the winner, you can afford to be big and Hillary should.”