Biden’s visit to New Jersey highlights an ongoing debate over SALT.

President Bidenwas in New Jersey on Monday to champion his efforts to pass legislation investing in early childhood education and passenger rail service. But the backdrop will highlight a still-simmering dispute among Democrats that is hampering Mr. Biden’s legislative agenda: whether to lift the limit on a tax deduction that largely benefits high earners in states like New Jersey.

Democrats — including the president, party leaders in the House and Senate and key factions of moderates and progressives in both chambers — are negotiating a package to spend an estimated $2 trillion or less on tax cuts and spending programs for child care, education, climate change and more.

A group of House Democrats from New Jersey have insisted that the package must include a change to the state and local tax deduction, known as SALT, which Republicans capped at $10,000 per taxpayer in order to help pay for their 2017 tax cut package. With a slim majority in the House, Mr. Biden cannot afford to lose more than three Democratic votes there in order for the bill to pass.

The SALT limit resulted in tax increases for some Americans, particularly higher earners from high-tax states, and helped Democrats capture some House seats previously held by Republicans in New Jersey, California and elsewhere. Many of those representatives are pushing to lift the cap now, a move that would likely amount to a tax cut for some high earners, at a time when Democrats are seeking to offset other revenue losses in the bill by raising taxes on corporations and the rich.

Negotiators have not yet reached agreement on a SALT provision. A big factor is the price of any potential change to the cap. It could cost hundreds of billions of dollars, which would put further pressure on Democrats to cut other spending programs in a bill that is shrinking dramatically from the president’s initial proposals, aiming to satisfy demands of centrists including Senator Joe Manchin III of West Virginia. But it remains a top priority for representatives like Josh Gottheimer of New Jersey and for Senator Chuck Schumer of New York, the majority leader.

Mr. Biden did not address the issue, or the state of negotiations, directly in a speech in Newark. But he outlined the benefits of his plans, leaning heavily into efforts to repair bridges and invest in passenger rail service, in an effort to win over voters in a state where Democrat Phil Murphy is seeking re-election on Nov. 2.

Mr. Biden stopped earlier in the day at an early childhood education center, where he talked with several children as part of an effort to spotlight a provision in the spending bill that would provide federally guaranteed pre-kindergarten for three- and four-year-olds.

Karine Jean-Pierre, the White House principal deputy press secretary, told reporters on Air Force One on Monday that Democrats have reached the point where they are negotiating “the nitty-gritty of the details” in the package and that Mr. Biden hopes to reach a deal before he leaves for an economic summit in Rome later this week.

“We have a strong base of agreement,” Ms. Jean-Pierre said. “We’re continuing to negotiate. We’re almost there.”