WASHINGTON — Senate Majority Leader Harry Reid expressed optimism Thursday about chances for compromise on jobless legislation, and officials said talks were focused on a scaled-back program that is fully paid for and would provide up to 31 weeks of benefits for the long-term unemployed.

The officials said the emerging compromise would run through the late fall, and the price tag — about $18 billion — would be offset through cuts elsewhere in the budget so deficits would not rise.

Rank and file senators in both parties were reviewing the proposal in closed-door noontime meetings.

The Senate has been working on a three-month resurrection of a program that expired on Dec. 28, immediately cutting off benefits of roughly $256 weekly for more than one million hurt by the recession.

Reid, D-Nev., told reporters he was “cautiously optimistic” about a compromise emerging later in the day, but provided no details.

The expired law provided a maximum of 47 weeks of payments after an unemployed worker has exhausted state-funded benefits, usually 26 weeks.

The new measure would reduce the 47 weeks to a maximum of 31 weeks, officials said, based on a sliding scale that dates to the expired program.

Officials said the first tier of additional benefits would be six weeks, and be generally available to all who have used up their state eligibility.

They said an additional six weeks would be available in states where unemployment is 6 percent or higher; an additional nine weeks in states with joblessness of 7 percent or higher; and 10 more in states where unemployment is 9 percent or more.

The cost would be offset in part by extending a previously-approved reduction in Medicare payments to providers, officials said, and in part by limiting or eliminating the ability of individuals on Social Security disability from also receiving unemployment benefits.

The officials who described the details of the possible legislation did so on condition of anonymity, saying they were not authorized to speak on the record. They stressed the specifics could yet change, and that the deal itself may fail to come together.