Chrysler Corporation said today it was slowing down production of the much-heralded K cars on which it has based hopes of surviving its financial troubles, and the bond rating agency Standard & Poor's Corp. lowered Chrysler's bond rating, citing "heightened uncertainty" about the company's ability to pay its debts.

Sales of the fuel-efficient, front-wheel-drive K car, launched in October, have been hurt by surging interest rates. Chrysler said it would lay off 2,880 workers at its K-car plants in Detroit and Newark, Del., when assembly lines start up again Jan. 12 after the Christmas-New Year break, and production will decline 21 percent from the pre-Christmas level.

Standard & Poor's action today is unlikely to have a major effect on Chrysler, which already is unable to borrow without a government gurantee. The rating on senior debt of Chrysler and its financial subsidiary was lowered from "B" to "CCC" -- both ratings indicating that the company is having financial difficulties.

S&P said the lower ratings reflect the "extreme pressure" on Chrysler "due to continued depressed auto sales and high interest rates, which have set back its recovery plan, accelerated the need to call on government guarantees and sharply reduced its net worth."

Chrysler, which has projected losses of $1.7 billion for 1980, is seeking an additional $400 million in loan guarantees from the federal government and a wage freeze from workers to save $600 million.

A Treasury Department spokesman said that the company's request for the new guarantees was expected today but that the Chrysler Loan Guarantee Board does not plan to meet on the matter until at least next week.

The spokesman said the delay is due party to the need for more time to study the request and partly because top Treasury officials have left for holiday vacations.

The new layoffs will mean that daily output will drop from 1,120 to 800 cars at the Detroit plant and from 1,120 to 960 at Newark.

Meanwhile, Volkswagen of America announced plans to hold down inventories by extending the Christmas production break at its two U.S. plants until Jan. 12. The production cuts at the assembly plant in West moreland, Pa., and the South Charleston, W.Va., stamping plant will be the first since the company began building cars in the United States in 1978. t

VW's U.S.-built Rabbit sold well after introduction as a 1979 model, despite the long slump the industry as a whole was entering. Last month, however, sales turned down with soaring interest rates, and invention stand at a 79-day supply.