Setting their sights on the next big delegate prizes, the presidential candidates descended on New York and Pennsylvania on Wednesday afternoon, with Senators Ted Cruz and Bernie Sanders looking to extend the momentum from their Wisconsin victories while Donald J. Trump and Hillary Clinton work to regain their footing after stinging defeats.

Mr. Trump and Mrs. Clinton, who still have wide delegate leads in the Republican and Democratic nominating contests, will be working furiously to win New York, where their opponents are devoting significant resources to try to score upsets in the delegate-rich state in its April 19 primary. With both candidates having deep roots in the state, losses would be especially painful. Mr. Trump, who has been uncharacteristically quiet on Wednesday, planned an evening rally that is expected to draw thousands of supporters.

A poll released Wednesday showed Mr. Trump with more than 50 percent support, and showing particular strength in New York City, Long Island and western New York. Still, the pressure is intense on Mr. Trump, who is enduring the most challenging stretch of his insurgent candidacy. His rally in Bethpage, Long Island, which is expected to draw up to 10,000 people, comes after a week of damaging questions about his treatment of women and knowledge of policy. And his double-digit defeat in Wisconsin further emboldened the Stop Trump movement within the Republican Party.