When given the opportunity, Sen. Arlen Specter (R-Pa.) didn't hesitate for a moment last week to apply more pressure to D.C. Mayor Marion Barry to build a new jail to relieve the nagging problem of inmate overcrowding.

During a luncheon meeting with Washington Post editors and reporters, Specter, chairman of the Senate Appropriations subcommittee on the District, was asked whether he planned to press the mayor a little to support new jail facilities.

"I'm not going to press him on it a little, I'm going to press him on it a lot," Specter said. "We have to have expansion and new facilities."

With the new budget season fast approaching, District officials will soon be making the trek to Capitol Hill to seek support for the city's fiscal 1986 budget. The controversy over conditions at the jail may prove to be a stumbling block to an amicable congressional review of the city's new budget.

Barry has repeatedly opposed proposals for new or expanded jail facilities, arguing that one of the keys to relieving overcrowding is to keep persons convicted of nonviolent crimes out of jail, sentencing them instead to make restitution to their victims or to perform community service.

City Administrator Thomas Downs also notes that the city has increased its capacity at the Lorton Reformatory in southern Fairfax County by 33 percent since 1980, adding 1,887 cell spaces at a cost of $28.5 million.

"We have done more than any other jurisdiction in the United States to increase our prison capacity," Downs said. "We have a right to say, 'Let's look at some alternatives.'"

The District's prison facilities at Lorton and the D.C. Jail were designed to hold a maximum of 4,881. This month, the combined capacity has been exceeded by more than 1,250. The city is under a court order to relieve crowding at the jail, but so far the mayor has not been moved to try to build a new facility.

Specter, a former Philadelphia prosecutor, argues that the city's long-term projections for a decline in the District's inmate population are far-fetched, in light of a new determinant sentencing law that likely will result in far more people going to jail for longer periods of time.

Specter, one of the chief congressional overseers of the city's budget and finances, has shown considerable interest in criminal justice issues in the District. His concerns about the need for a new jail are bound to carry great weight.

"I do not believe the mayor will be adamant against it," Specter said last week with notable confidence. "When faced with the evolving factual picture, Mayor Barry will agree we need additional facilities."

The sometimes fractious City Council and its chairman David A. Clarke apparently scored a victory by maintaining harmony while dealing with some sensitive issues during its recent organizational meeting.

Council members generally were satisfied after the closed-door meeting and Clarke got approval for two significant changes.

The council accepted his proposal to hire, at a cost of $44,929 a year, an intergovernmental liaison officer to monitor congressional legislation for the council.

Last year, when Clarke introduced the same proposal, it was rejected. At that time, some council members feared that the main result would be an additional staff member for Clarke.

Some council members said they felt that they were very late in understanding the seriousness of this year's lengthy debate with Congress over the city's home rule charter. Until that issue was resolved, the city could not issue tax-exempt bonds.

Clarke also succeeded in getting the council to transfer jurisdiction over alley closings from the public works committee to the committee of the whole, which oversees other land-use matters and is chaired by Clarke. The transfer was apparently made without a major debate, despite the fact that alley closings are closely monitored by the real estate and development community and will certainly be viewed as a new source of power for Clarke.

City Council member Nadine P. Winter (D-Ward 6), who will become the new public works committee chairman, raised the major objections.

While council members did not receive all they wanted, through a series of tradeoffs that involved exchanges of office space and committee assignments they got enough to make them content.

H.R. Crawford (D-Ward 7), whose committee was given responsibility for oversight of the D.C. Lottery Board, said that Clarke managed the meeting well.

"I would give him an overall A+," said Crawford. "The meeting went extremely well and it was a very good working meeting."

John Wilson (D-Ward 2), on the other hand, gave much of the credit to the group.

"I think the council had an open discussion and did what it thought was best in every situation," Wilson said. "I don't think it was a question of anybody's leadership."