Gov. Andrew M. Cuomo, who controls the subway, supports the plan, and he convinced state lawmakers to approve congestion pricing tolls in Manhattan to help pay for it. But it is not clear whether Mayor Bill de Blasio or the Trump administration will make major contributions.

There is also the question of how best to install modern signals. The transit agency has previously used a technology known as communications-based train control, or C.B.T.C. Mr. Byford favors that method and says he can put it into effect more quickly than his predecessors, but Mr. Cuomo has pressed the agency to look at other methods, including a technology called ultra-wideband that has not been used on major transit systems.

If the capital plan moves forward, the routes set for signal upgrades are the busy Lexington Avenue line in Manhattan, including the 4, 5 and 6 trains; the A and C lines in Brooklyn; the N and W lines in Queens; the E and F lines in Queens; and the G line in Brooklyn and Queens.

Many of the neighborhoods served by those trains, from Bedford-Stuyvesant in Brooklyn to Jamaica in Queens, are working-class or middle-income areas that have longed for better subway service. And while the subway has started to recover from a deep crisis, some lines are still worse than others.

Gerson Amaya, 42, a carpenter who lives in Brooklyn, said that his commute to Inwood on the A train was long — “long enough for a nap.”

“Any delays on top of it just makes it worse,” Mr. Amaya said as he rode the A on a recent morning. “There’s always a signal down or some issue.”

Susan Roy, 45, a wine buyer who lives in Richmond Hill in Queens, said that the A train had not received the attention it deserved.