Chrysler Corp. will have to sell virtually every 1981 model front-wheel-drive compact and subcompact it can build to survive financially, the government's loan guarantee board has concluded.

The board, in approving $1.5 billion in federally guaranteed loans to Chrysler Saturday, has taken what it called a calculated gamble that Chrysler can achieve the sales goals.

The board's detailed analysis of Chrysler's prospects and the $2 billion in nonfederal assistance Chrysler has obtained, was released yesterday by the Treasury Department and sent to Congress.

Treasury Secretary G. William Miller, chairman of the Chrysler loan board, is expected to be questioned closely by Congress about the auto company's survival prospects and the economic assumptions on which the aid plan rests. Sen. William Proxmire (D-Wis.) chairman of the Senate Banking, Housing and Urban affairs Committee, has asked Miller to testify on the plan next Tuesday.

Federal Reserve Chairman Paul Volcker and Comptroller General Elmer Staats, the other two voting members of the board, have also been asked to testify.

Proxmire, in a statement yesterday, pointed to Chrysler's fast-deteriorating condition this year in questioning the board's conclusion that the company can recover.

The loan guarantee board, in effect, paints a "before" and "after" picture of Chrysler, in predicting its survival. The board estimates Chrysler's losses this year will total more than $1 billion, as car buyers continue to turn their backs on the company's full-size cars and trucks.

But with the introduction of Chrysler's new front-wheel drive K-body compacts this fall, joining the existing subcompact Omnis and Horizons, Chrysler can return to profitability, the board concluded.

"The assumption is they will sell every last K-car they can produce," said a high-ranking Treasury official who briefed reporters yesterday on the board's findings. Chrysler will probably have to sell its full-size cars and trucks at cost, or with little profit, in order to move them, the official said.

The K-car is a four-cylinder, front-wheel drive compact that is expected to be rated at 35 miles per gallon. It will compete directly with General Motors Corp.'s X-cars, the Chevrolet Citation, the Buick Skylark, the Pontiac Phoenix, and the Oldsmobile Omega.

The board said that Chrysler is certain to price its K-cars very close to the industry price leader, General Motors.

Prices on the fuel-efficient compacts have risen sharply, the board noted. The Citation's price, for instance, has risen 20 percent since its introduction a year ago. (Similarly, Chrysler has boosted the price of its four-door subcompact Omnis and Horizons by an average of 23 percent since the end of the 1979 model year.)

Chrysler's profitability depends upon its ability to sell the K-cars at a relatively high price, comparable to General Motors' prices. And this, in turn, depends on a strong, continuing demand for light, fuel-efficient cars by car buyers, the board acknowleged.

The board estimated that Chrysler will sell 973,000 cars in 1980, and 1.36 million in 1981 in the U.S. and Canada, slightly less than the assumption by Chrysler. The first year production of K-cars is estimated at 550,000.

In 1978, before the market for mid- and full-sized vehicles collapsed -- Chrysler sold nearly 2 million cars and trucks.

There is some breathing room in the Chrysler operating plan approved by the board, the Treasury official said. The board estimated that Chrysler will require $1.1 billion in federally guaranteed loans, leaving $400 million in loan authority unused.

If the economy deteriorates from the moderate recession the administration forecasts into a deep slump like that in 1974-75, the remaining $400 million would be available to help Chrysler stay in business, the loan board said.

Although Proxmire and other critics aren't happy with the Chrysler rescue plan -- particularly the reduced contribution of new credit by Chrysler's lenders -- their options for halting the first phase of the bailout appear limited.

But the board's action Saturday approved only the first $500 million installment of the $1.5 billion loan authority, and Proxmire and Republican Senate allies are likely to attempt to impose new conditions on Chrysler's lenders and creditors before the full amount of the loan guarantee is drawn.