Shortly before the board meeting, subway riders suffered through another morning of painful delays.

John Raskin, the executive director of the Riders Alliance, an advocacy group for passengers, welcomed the increased commitment to the transit system, although he said he was concerned about the lack of urgency regarding subway service.

“Investing in the M.T.A. is a good thing, but these changes won’t address riders’ core concern of the increase in crowding, breakdowns and delays,” Mr. Raskin said.

In a private meeting before the vote, there was a contentious debate among board members about the capital plan and doubts about its ability to pass, according to a person who was present for the discussion but not authorized to discuss it publicly. Board members raised concerns about the agency taking on additional debt and about whether the plan aligned with what the public had been demanding, the person said.

The authority’s chief financial officer, Robert E. Foran, said the plan would increase the agency’s debt by about $5 billion, to about $42.5 billion. Mr. Foran said the increased debt would not require the authority to raise fares and tolls beyond gradual increases scheduled to take place every two years.

“This is not putting any additional pressure on fares and tolls,” Mr. Foran said.

But some board members were not mollified. Veronica Vanterpool, one of two board members nominated by Mayor Bill de Blasio who voted against the amended capital plan, said she did not think the authority should have to take out more debt to finance the proposals.