Mayor Marion Barry's last-resort plan to pay off the District government's cash debt through a long-term bond issue received strong support from the Reagan administration and tepid endorsement from New York financial experts yesterday, but a key member of Congress said there is no possibility of congressional approval.

Rep. Stewart McKinney (R-Conn.), ranking minority member of the House District Committee, said he could not ask his House colleagues to vote for legislation authorizing the $184-million bond issue when, he said, the District has not imposed order on its tangled financial affairs and has less costly alternative ways of raising the money.

City officials fear that McKinney's opposition could leave the bond bill with slim chance of passage. Its defeat would knock out a vital prop of Barry's overall financial rescue program and leave the city desperately short of money to meet payrolls and welfare payout cycles. Del. Walter E. Fauntroy (D-D.C.) said he hoped McKinney would change his views in light of the support for the bill expressed by Reagan adminstration officials. l

Roger W. Mehle, assistant treasury secretary for domestic finance, told a House D.C. subcommittee that the administration favors enactment of legislation that would permit the city to seel the bonds to pay off old debts. He said that "the administration believes that the District should be managing its own finances" and the bond proposal is consistent with the overall policy of detaching the District from federal purse-strings.

He said the terms under which the bonds would be sold "are reasonable" and that "the administration strongly supports the District's efforts to enter the bond market."

McKinney, however, said the House would not accept the bill when the city has surplus land that it could sell and has failed to balance its budget. Even if Congress approved the bill, he said, the bond sale process could not occur before Sept. 30, the date by which Barry says the city needs the money. Moreover, McKinney says he does not think the bond authorization would bring in any money, because the bonds would not find buyers in the city's present financial condition.

In an effort to win congressional approval of the bond issue that Barry says is the only workable solution to the urgent cash deficit problem, the mayor has committed himself to balancing the budget every year from now on, and has offered to amend the bill to state specifically that the federal government could never be called upon to pay off the bonds if the city defaulted. But McKinney said that is not enough.

"I can't find a single member of the House who believes the city is going to balance its budget or who doesn't feel the city views the federal treasury as the court of last resort," he said. McKinney, who was deeply involved in the legislative fight over federal aid to New York, said he knows what questions House members will ask before voting for the bond authorization and the city does not have the answers.

"Nobody wants to see the city go into the bond market more than I do," he said. "But is Congress going to let them? No. Can they get into the bond market in this condition? No."

McKinney said the city should limit its borrowing to capital projects. He said the deficit should be paid off by selling the site of the downtown campus of the University of the District of Columbia, which he said will never be built, by raising taxes and cutting payrolls, and by using some of the new revenue sources expected to be available next year, such as a one-time windfall from the seizure of dormant bank accounts.

He said that is far preferable to the city's plan to borrow the $184 million and pay it off over 20 years. "Debt service is the greatest burden, the most onerous thing you can put on citizens. It robs them, it's unfair and somewhat obscene," he said.

If Congress does approve the bond issue over the opposition of McKinney and his Republican colleagues on the District committee, the bonds probably can be marketed, but only after intensive scrutiny by bond-rating agencies and a vigorous sales promotion campaign by the underwriters, the New York financial experts testified.