Between the troubled Chrysler Corporation and sudden-death bankruptcy there has now been interposed a political game. At issue is whether the blood finally shows up on the hands of the outgoing or incoming administration. Whatever the outcome, the lesson is that the American system lacks good machinery for dealing with private corporations that fail with sweeping public consequences.

At present Chrysler is operating under the conditions of a government-guaranteed loan of $1.5 billion. The company has already drawn $800 million of that sum. Its plan for recovery presumed a positive balance sheet for the fourth quarter of this year. On that assumption, the company figured it would not have to ask for any further installments on the guaranteed loan until spring -- if at all.

But the fourth quarter has turned sour. There has been at least some resistance to the high sticker price (over $9,000) on Chrysler's new K-cars. High interest rates dull the appetite of buyers still further, and make dealers reluctant to accumulate inventory.

The outlook for the fourth quarter, instead of a gain, is for a loss of at least $100 million. "I have a feeling," the company chairman, Lee Iacocca, said in a recent interview here in Detroit, "that we are heading into a wall of solid concrete."

To avert a smash, Iacocca is calling on the federal government to free another $200 million of untapped loan funds by Jan. 15. He argues that if the money is not forthcoming at once, the company will go bust. While that claim may be right, there is also a political consideration in the timing.

In the legislation authorizing the Chrysler loan, Congress established a supervisory board of three persons -- the secretary of the Treasury, William Miller; the chairman of the Federal Reserve Board, Paul Volcker; and the head of the General Accounting Office, Elmer B. Staats. Before releasing any of the loan money, the board must find that the company is "viable" -- that is, that it has at least a chance to become healthy again. The statute further provides that the decision must be rendered 15 days before the release of funds. Thus the latest Chrysler request calls for a decision by the present board before Jan. 1. It cannot be deferred for the Reagan administration.

Miller favors release of further funds to Chrysler. He has been the chief advocate of the Chrysler loan all along, and is predisposed that way on the merits of the case. But it also has to be noted that if the loan were granted now, any further Chrysler troubles would be charged to the account of the Reagan administration.

Volcker and Staats head independent agencies supposedly above partisan politics. By temper and conviction, both men are more cautious than Miller. They have expressed doubts about Chrysler in the past, and they would be sensitive now to the risk of throwing good money after bad.

At that point the incoming administration enters the picture. Any sign of opposition to the loan on the part of President-elect Reagan would undoubtedly carry weight with Volcker and Staats. As it happens, the incoming team has a couple of reasons for being negative. A bankruptcy now would charge the Chrysler problem to the account of Jimmy Carter.

Exactly what will happen in these conditions is now clear. The company could be allowed to go down soon. A more likely outcome -- considering the number of jobs involved and the big stakes held by such public bodies as the city of Detroit and the state of Michigan -- is that a further dispersal of the loan will be voted. But with conditions that make success even more difficult -- especially since Chrysler now has to borrow at the going interest rate of about 20 percent.

In either case, the best alternative will not have been available. The best alternative would be for the government to acquire shares of Chrysler in return for financial help. Chrysler would then get its money without having to pay heavy interest charges.

If bankruptcy loomed, the government would be in position to deal with various buyers -- Japanese or European auto companies, in particular -- so they could take over parts of Chrysler. In that way most of the jobs could be saved. The interested public bodies would be afforded maximum protection.

But, of course, for such a smooth handoff to occur, this country would have to remedy a major defect in the system. It would have to develop a coherent industrial policy and a regular institution -- something like the old Reconstruction Finance Corporation -- for administering that policy.