The precarious state of Metro's finances and the fragile nature of the regional coalition that was formed to build a subway and then found itself also operating the area's buses, was never more evident than yesterday.

Metro board members, in a fury over another federal letter, directed general manager Theodore Lutz to get the federal government off their backs, if he could.

Then they picked a committee to draft an agenda for a regionwide meeting of top elected officials who would, the board hopes, wrestle with Metro's divisive financial problems and then reaffirm the spirit of regional unity necessary to solve them.

And Montgomery County Executive James P. Gleason announced he was releasing the last of the Metro construction money he had been withholding in an attempt to get an ironclad federal commitment to extend the Red Line from Silver Spring to Glenmont.

At one time, Gleason had more than $400 million in federal and local money tied up. He was down to $15 million yesterday. He still does not have an ironclad guarantee for the Glenmont line, but the line's prospects look better than they did six months ago if the region can tie up Metro's financial loose ends.

That list is as good a commentary as there is on the disparate problems Metro faces today.

The Carter administration, pledged to a balanced budget by 1981, is perceived as a foe of subway construction programs. Whether that is correct, it is clear that President Carter is the first Presddent since Metro construction started not to have made a public pledge to complete Metro's full 100-mile system.

Local governments here, pushed to the wall by demands from citizens that their property taxes not be increased, have only the property tax to use to pay the increasing operating deficit of Metro's bus and subway systems.

Taxes other than the property tax that would be earmarked for transportation are gaining theoretical support, but are a long way from being implemented. Virginia politicians feel they have a chance to get a 4 per cent gasoline sales tax for Northern Virginia in the next legislative session. But both Maryland and the District of Columbia have elections, and new taxes of any kind don't fly well in election years.

The entire Metro subway system beyond the 60 miles either under construction, now operating, or funded is receiving careful restudy at the order of the federal government. That study, called "alternatives analysis," will certainly resulted in some changes to the now planned 100-mile system and may well result in some shortening.

When that happens, some of those counties that contributed money for construction of Metro back in 1968 but do not have Metro will want their money from the others, and all the money is spent. That bullet has been too rough to bite so far, because everyone in that region is eager to keep everyone else in.

"Alternatives analysis," Metro board member Carlton Sickles said yesterday, "is nothing but a trap . . . It has kept us from bringing the entire community together."

"To climb out of that trap," board member Joseph Alexander said, "we will have to have some details of what the system will look like."

"This program is in a state of crisis," said board member Cleatus Barnett. "There is a strong likelihood we will not build a single mile beyond the 60 during the term of the current President . . . Metro is well on its way to going down the tubes."

In the depths of the depression was born the proposal for a regionwide meeting, presumably so Metro board members can share their misery with company.

The entire discussion was triggered by a resolution that Lutz must sign so Metro can pay the $26.2 million in interest on construction bonds due Jan. 1.

Most of that money, $22.9 million, is federal, but the rest comes from Metro. In theory, all the interest was supposed to be paid by revenues collected from a smooth-operating subway system. Instead, the federal government, about which everybody is getting so exercised, has had to bail out Metro and itself. The federal government has guaranteed the bonds.

In the process, Congress demanded that Metro get its financial house in order and devise a scheme to retire the $1 billion in bonds that are outstanding. It is estimated that over 30 years, it will take $2.5 billion in interests to service the bonds.

To expedite the January payment, Lutz and his associates drafted a resolution, then sent it over to the Urban Mass Transportation Administration (UMTA), an agency of the Department of Transportation. UMTA would look at it, everybody would agree in advance, and the payment would slide through.

UMTA sent the resolution back with some hooks attached. In a letter signed by C. Russell Scoville, UMTA said the resolution should incorporate language binding Metro to a deadline of June 30 to complete a full financial plan and to satisfy other federal requirements.

Scoville's name is a red flag for many board members. They see him as a single-minded trying to dismantle the Metro system from his tenured slot at UMTA. Administrators and secretaries of transportation come and go, but Scoville oversees the Metro program. Scoville steadfastly denies 11 such charges and says he's doing his job of protecting the federal interest.

So the board told Lutz to go see Scoville's boss, Richard Page, and negotiate. The June 30 deadline, Alexander said, "is impossible; we don't even know how much subway to plan for yet."

Other board members, including Joseph Wholey, said they think it might be possible to reach such a deadline.

In any event, Page said in a telephone interview that, yes, he had seen the letter Scoville sent over to Metro. Further, he said, "I am not wedded to June 30. But I am wedded to having commitment from (the Metro) boad that they are working seriously on the development of a financial plan. I haven't seen any evidence there is any analytical effort under way. . . "

Page conceded there is a "chicken-egg problem" with alternatives analysis, but said that some elements, of a financial plan, such as the revenue bonds, entailed known costs and could be solved earlier.

Gleason announced he was releasing the construction money during the board meetin yesterday after Barnett told him that the regionwide meeting was being organized. He released the money, Gleason said later, because of the prospect of that meeting. "I think its important to keep metropolitan wide support," he said.

As the Metro board meeting rolled into its third hour yesterday, a financial plan for the syatem, drafted by Lutz, was introduced for discussion. By the time 15 minutes had passed, the board was down to three members - Wholey, Barnett and Douglas Schneider. The board has 12 members; 11 of them attended yesterday.