The head of the council representing commuters warned of the political consequences. Commuters need to hold lawmakers “accountable for the potential fare hikes and devastating service reductions on the branches and if this issue is not fixed; they need to remember this at the polls on Election Day,” said Jim Gildea, the chairman of the Connecticut Commuter Rail Council.

Connecticut relies on a state transportation fund to pay for roads and public transit. But the fund has seen its resources dwindle since 1997, when the state lowered its gasoline tax, cutting total revenue by $4 billion, according to the office of Governor Dannel P. Malloy. An increase in vehicle gas mileage and a growing market for electric cars has also led to a drop in gas tax revenue.

In 2016, a state panel recommended increasing the gas tax to 39 cents a gallon from 25 cents over a seven-year period, raising fees charged by the Department of Motor Vehicles and reintroducing highway tolls, which Connecticut removed in the 1980s. The report has not led to those changes yet. Mr. Malloy proposed several measures this week to raise money, including a return of tolls and a 7-cent-a-gallon increase in the gas tax.

Mr. Redeker called the tolls a longer-term solution that would take at least four years to put in place and would not alter the July 1 changes to train schedules.

Mr. Malloy’s office recently froze hundreds of transportation-related capital projects that total $4.3 billion and vary in scope, from the replacement of salt shed roofs to the widening of Interstate 95 between Bridgeport and Stamford. One project that is still moving forward is an expansion of a rail line linking New Haven and Springfield, Mass., that is intended to spur development and ease highway congestion.

The threat to eliminate weekend service comes even as demand for railroad service in Connecticut has grown. From 2005 through 2016, the last year for which data was available, annual ridership on the New Haven Line rose about 19 percent to 40.48 million from 33.89 million. During that period, annual ridership on the three branches increased about 14 percent, to 2.6 million from 2.3 million. Weekday ridership on the Waterbury line averages 960; on Saturdays, the average is 834.