The University of the District of Columbia may delay classes next fall by one or two weeks to keep from running out of money before the end of this fiscal year.

Lisle C. Carter Jr., the university's president, told the D.C. City Council yesterday that such a move "is clearly not a desirable solution" to help the city's budget deficit, because it only pushes this year's costs into the next fiscal year.

"Nevertheless, it seems preferable to furloughing employes," Carter said, "or to the damage that would be done to the educational plans of students by [totally] eliminating summer school or reducing it below 50 percent of last year. University trustees already have voted to cut the school's summer program nearly in half.

Carter testified as the City Council opened two weeks of hearings on Mayor Marion Barry's proposals for raising taxes, cutting programs and his request to Congress for a $62 million supplemental appropriation. Earlier in the day, the mayor explained his proposals to the council -- and got a mixed reaction.

Willie J. Hardy (D-Ward 7), a longtime political adversary of Barry, criticized him for giving pay raises to five high-ranking members of his staff just five days before he imposed a freeze on hiring and promotions last month.

Hardy said her constituents want to know, "Why isn't he giving it [the money] to the [Department of] Corrections so somebody can keep a job?"

Under the mayor's proposals, the corrections department faces 360 layoffs, including guards at city jails.

John A. Wilson (D-Ward 2), chairman of the council committee that must review Barry's proposals to raise $20 million in taxes this fiscal year, called that program a piecemeal approach. He urged the mayor to broaden his program into one offering permanent financial solutions.

Barry suggested that Wilson draft his own plan "and float it." Wilson said that reply indicated the mayor is "probably. . . willing to go further" than his own plan implies. Barry responded: "Yes, if I can get support."

The mayor's proposal calls for six new or increased taxes, including a 5 percent sales tax on various professional and consumer services, and a 6 percent sales tax on gasoline. In addition, he would raise $4 million by increasing various city fees.

Hilda Mason (Statehood-At-Large) suggested raising personal income taxes in the higher brackets, with an early increase of withholding deductions from taxpayers' wages. That's something to look at," the mayor replied.

Jerry A. Moore Jr. (R-At-Large), the council's only Republican, promised a sympathatic hearing for the mayor's program. Council Chairman Arrington Dixon (D) said he would not want to be remembered in local history books for letting the city collapse financially.

Barry has acknowledged that the city's financial shortfall could grow as large as $172 million, this fiscal year, but he reasserted yesterday that the gap, in his view, is only $92.6 million.

And even if that gap is filled, administration officials acknowledged at yesterday's hearing, the city will wind up the current fiscal year with more than $23 million more in expenditures than it took in through revenues.

City Budget Director Gladys W. Mack, who also appeared at yesterday's hearing, said that the $23 million was an improvement over 1979, when the government spent $41 million more than it took in. "We're improving our fiscal health," Mack said, "although we recognize we still have a way to go."

Council member Betty Ann Kane (D-At-Large) disagreed. "Even with the tax increases, even with the budget reductions, even with the cuts, even with the freeze," Kane said, "we're not going to pay all our bills by the end of this year."

Kane also was critical of other figures indicating that while the Barry administration had anticipated having $152 million in unpaid bills on hand when the current fiscal year began Oct. 1, the amount was $162 million instead. "We're falling further behind," Kane said.

Mack said, however, that those figures were not a fair barometer of the District's financial health. "What is it fair to say," Mack said after the hearing, "is that the city obligated itself to pay $162 million but did not actually write the checks."

The council hearings that began yesterday dealt chiefly with cost-cutting at UDC and in the public school system .

Carter said UDC already had taken steps to cut about $5 million, or about 10 percent of its annual budget, when the mayor asked for further cuts of $1 million. The mayor also will ask Congress for a $1.3 million supplemental appropriation for the university.

Unless the supplemental appropriation looks likely by next month, Carter said, the university's trustee probably will consider opening the school late next fall. That means faculty would report around Sept. 30 instead of Sept. 16, with the added time -- and faculty wages -- to be carried over into next fiscal year.

School board president R. Calvin Lockridge testified that the mayor's proposed $6.1 million cut in the school budget "could have devastating consequences on the education of children."' But he said the school board "has yet to contemplate the possibility of . . . a reduction" and he does not know where its effects would be felt.