UNION BEACH, N.J. — It was a rare convergence of New Jersey’s governor and its two senators for an official event meant to be about policy, not politics.

But as Gov. Philip D. Murphy announced new programs to help homeowners recover from Hurricane Sandy, there was little doubt why the state’s top Democrats had convened so soon before Election Day.

“I don’t know where we would be without Senator Bob Menendez,” Mr. Murphy said. He was followed by Senator Cory Booker, who offered his own lofty praise: “When I look to the future of this state, we need Bob Menendez.”

Democrats are poised to win a number of governorships across the country and perhaps control of the House on Tuesday, thanks in large part to a suburban backlash to President Trump. But in a state rich with commuters and cul-de-sacs, party leaders are being forced to mount a last-minute, all-hands-on-deck effort to rescue Mr. Menendez’s candidacy and preserve their long-shot dreams of a Senate majority.