The new Reagan administration early next year will be caught between a rock -- its economic policies -- and a hard place -- its political interest in the future of Chrysler Corp. and other troubled American automakers.

Although President-elect Ronald Reagan endorsed the government bailout of Chrysler in the campaign, reversing his initial position, he has not changed his fundamental belief that automakers should stand on their own without government backing, aides say.

And Chrysler, the nation's No. 3 vehicle builder, is not exactly standing on its own. It already has received $800 million in federally guaranteed loans and soon will need another transfusion, probably a large share of the remaining $700 million approved by Congress.

The new K cars, on which the company's survival depends, are selling far below the minimum rate set out in the company's plan for recovery. The company had hoped to begin making a profit by the end of this year, but now faces continued losses running into 1981.

Under the rules of the government bailout, the federal government can guarantee loans for Chrysler only if there is persuasive evidence that the company is a going concern with a profitable future in sight. But unless the economy makes an unexpected rebound soon, Chrysler's prospects will not look good next spring when the Reagan administration must take a stand on whether to aid the company.

The sluggish pace of auto sales also has pushed American Motors Corp. into a financial crisis, and Ford Motor Co. is likely to fall farther and farther behind General Motors unless imports of Japanese cars are restricted, says United Auto Workers president Douglas Fraser.

If Ford's sales don't improve, the company will be pushing hard in Congress for action to restrict Japanese imports, confronting the Reagan administration with another difficult choice between following a free market philosophy and backing an important, visible industry with considerable political muscle.

Reagan's economic advisers don't predict how he will handle the problems of Chrysler and the other auto companies. The last thing they expect Reagan to do is pour more federal support into the industry while also cutting back on the government's spending and credit activities, although some think Reagan would approve the last $700 million for Chrysler.

Auto analysts, however, think more federal support may be critically needed.

Chrysler's recovery plan assumes that the company can sell its entire line of 1981 K cars, the compact Dodge Aries and Plymouth Reliant, which went on sale in October. The target is 38,900 K car sales a month, with overall sales for all models of 74,000 a month this year and 101,500 a month next year.

So far, Chrysler is nowhere near those targets.

K car sales in October totaled 18,272. The cars got off to a fast start, with 15,267 sales in the first weekend that they were on display at dealerships. But sales in the first 10 days of November totaled only 3,877.

Sales of Chrysler's subcompact Dodge Omni and Plymouth Horizon, which slumped last summer, have not yet rebounded. Chrysler now agrees with industry analysts that it made a mistake in loading many of the first K cars with expensive extras. This made them a gaudy item in showrooms but also saddled them with price tags of $7,500 and higher. Although Chrysler boasts that a stripped-down K car, with a base price of $5,580, is the "best buy in the world," that's not what it was showing potential customers last month.

Production runs are being altered to turn out cars with fewer options and lower prices, but Chrylser can't cut too far because K car profits are crucial to the company's recovery.

Most auto industry experts are not writing Chrysler's death certificate. "I suspect they can get to operating profitably," said Arvid F. Jouppi, an auto inudstry analyst. "I look for Chrysler to right itself, as soon as it breaks even and begins to make a little money."

What Chrysler and its hard-hit competitors need, more than guaranteed loans, is a sudden economic recovery that puts consumers in the mood to buy cars once more. But a quick economic fix is not in the president-elect's economic plan, says his chief domestic adviser, Martin Anderson. It may be the end of 1981 before significant economic improvements show up, Ronald Reagan's transition chief Edwin Meese told reports last week.

The U.S. car industry is still struggling to escape the 1980 recession. Sales by domestic producers are lagging badly at an annual rate of between 6.6 million and 7 million cars, according to estimates by leading auto analysts -- far below the 8.8 million sales level hoped for last summer.

And now, worried auto executives see their companies trapped by a return of the high interest rates that crippled car sales six months ago. The prime lending rate, which had dropped to 11 percent briefly in August, is now back at 17 percent.

As long as there is hope for a general improvement in the economy, there is some hope for Chrysler, says David Healy, an auto industry analyst with the Wall Street investment firm Drexel, Burnham, Lambert.

"If Chrysler can take down the remaining $700 million [in government guaranteed loans] they probably can get through next year," said Healy.