Key Senate committee members indicated yesterday they will let Office of Management and Budget Director Bert Lance out of his promise to sell a block of bank stock by next Dec. 31.

Lance made the promise at his confirmation hearing to avoid possible conflict of interest. But he could lose millions of dollars if he complied, and President Carter Tuesday asked Congress to give him more time.

Carter's request and the sympathetic attitude on the Hill apparently provided a tonic for Lance's affected National Bank of Georgia stock, meanwhile. In the past two days the bid price of the stock has advanced $2 to $11.25 or a recovery of about $400,000 of Lance's "paper" loss that had reached $1.6 million.

Ther is no chance Lance will resign. White House press secretary Jody Powell told reporters yesterday. Lance said that if Congress holds him to the deadline, the stock will be sold and he will stay at his OMB job.

The financial and political dilemma revolving around Lance's National Bank of Georgia stock apparently will be resolved, at least temporarily, after a hearing Friday by the Senate Governmental Affairs Committee, at which Lance will testify.

Chairman Abraham Ribicoff (D-Conn.) and Committee members Henry Jackson (D-Wash.) and Charles Percy (R-Ill.) are known to be willing to extend the deadline, barring some new evidence of a clear-cut conflict of interest.

Even if the committee removes deadline pressure, the problem still exsist. For one thing, Lance told reporters yesterday that the trustee holding the NBG stock expects to seek a private sale, presumably at a price above the regular market. He said that a reporter who implied such an above-market sale might put him under obligation to the purchasers was not "fair at all."

"Lance holds 21 per cent of the bank's stock, and therefore "there never was any intention to dispose of the stock except through private placement, and that's the way it will be handled," the OMB director said. He said all details of a private sale, including the price paid and names of the buyers, would be made public.

Although the NBG stock, along with other assets of Lance and of his wife> LaBelle, were reportedly placed in a "blind trust" last January. Lance said yesterday that he has "permission" from the Senate committee "to engage in discussion of the sale of the stock."

He told a reporter that "I would expect that if the trustee had a customer for the NBG stock, he would call me." He said that was part of the understanding leading to his acceptance of the Dec. 31 deadline, a requirement that exceeds federal statutes or guidelines laid down for other federal officials, including Special Trade Representative Robert Strauss.

If the Senate Committee abandons the deadline, it is not clear how long Lance of his trustee intend to hang on to the stock.

Lance's press aide, Robert Dietsch, said he assumed that the trustee would make a "prudent and diligent effort" to sell the stock, but acknowledged that it was "possible," if no such sale proved feasible, that the trustee might hold the stock.

The touchy problems relating to the Lance stock holdings arose when Lance agreed, on his appointment to OMB, to the sale of the NBG stock by a trustee no later than Dec.31, 1977. Other administration officials were required only to place their assets in trust, with no sales requirement.

Lance said yesterday that he "simply had been first [among administration appointees]," and that less stringent guidelines had evolved later.

Since Lance borrowed $2.7 million in 1975 and 1976 to buy the NBG stock at an average of $17 a share, or close to $3,250,000, the market value has plummeted. At one point last week, it was as low as $8.50 or half of what Lance paid.

The knowledge that a large block of the thinly-traded NBG stock would soon come on the (over the counter) market has been a collateral factor depressing the value of the shares. A principal cause is that the bank's operations have recently shown a loss.