The House decided yesterday against building itself a new parking lot that had stirred opposition from Capitol Hill residents, and then came within a hair of defeating the congressional leadership's controversial plan to extend the west front of the Capitol.

In an unexpected move, Rep. Frank Thompson Jr. (D-N.J.), chairman of the House Administration Committee, asked that the parking facility proposal be withdrawn. The parking lot was proposed for the vacant former site of Providence Hospital at 2d and D Streets SE.

Thompson said he became convinced the project was a bad idea after getting a letter opposing it from Del. Walter E. Fauntroy (D-D.C.). That led him him to visit the site and talk to several Capitol Hill residents, who objected to the proposed parking lot because they said it would cause additional traffic and pollution.

"It would be an improper use and unfair to the area," Thompson said on the House floor yesterday, "I am glad I have changed my mind."

Later in the day, following two hours of sometimes sharp debate, the House voted 212 to 204 to spend $55 million to extend the center of the Capitol by 22 feet, covering over the last remainining visible section of the original 177-year-old building.

In fact, the original roll call, taken by an electronic tabulating device, resulted in an apparent defeat of the west front project by a vote of 203 to 201.

House leeaders, including Speaker Thomas P. (Tip) O'Neill (D-Mass.), strode about urging opponents of the project to switch votes. Enough did to change the result.

Both projects were included in a $928 million appropriation bill to finance operations of the House - and of several congressionally related agencies - during the fiscal year that begins Oct. 1. The bill was approved, 250 to 161, sending it to the Senate, where the west front project has been defeated in the past and faces strong opposition again.

House opposition yesterday was led by Rep. Samuel S. Stratton (D-N.Y.), a foe of even more ambitious Capitol extension plans in the past. He said the modified version now being proposed would "destroy the shape of the Capitol."

The west front is the facade of the Capitol that faces downtown Washington and the Mall. Constructed of sandstone, it has deteriorated badly and has been shored up with heavy timbers.

Even critics of the extension agreed something must be done to improve the facade. They favor restoration and preservation efforts. Capitol Architech George M. White has estimated that restoration would cost $45 million.

The decision not to build the $483,000 parking lot for 400 congressional employee's cars on the Providence Hospital site was a victory for the Capitol Hill neighborhood, which lobbied against it.

Phoebe Bannister, a leader of neighborhood opposition, who listened to yesterday's debate from the House gallery, said she was surprised and delighted by Thompson's statement. "I think it shows when you get facts before intelligent people, they act reasonably and rationally," she said.

Thompson said he is constantly deluged with requests to issue more parking permits, and that his committee "will continue to look for more parking spaces in a more appropriate area."

He told a reporter, however, that he will be in no hurry to do so, since he wants to see whether Metro subway service - which will start running to Capitol Hill Friday - may reduce the need for more parking.

The appropriation bill, for the first time, was broken into separate chapters covering congressional operations, related agencies such as the Library of Congress and the Government Printing Office, and capital spending items, such as the west front extension.

This was done, according to Rep. George E. Shipley (D-Ill.), chairman of the Legislative Branch Appropriations Subcommittee, to deflect public and media criticism of "the billion-dollar Congress."

While the total appropriated will ultimately be $1.1 billion, $492 million will be for actual operation of the House and about $200 million for the Senate.