House Republican leaders, in a second try at passing a budget for fiscal 1983, reached tentative agreement yesterday on a plan designed to produce a deficit of less than $100 billion.

It would soften earlier proposals for cuts in several popular programs such as Medicare and make up the lost ground by cutting deeper into welfare and other programs for the poor and shaving proposed defense spending, Republican sources said.

Taxes would be increased by no more than the $20 billion included in the earlier Republican budget proposal, according to House Minority Leader Robert H. Michel (R-Ill.).

A pay raise of 4 percent would be allowed for federal workers, or 1 percentage point less than the House tentatively approved last month. But, in accord with another tentative House vote, a proposed "cap" of 4 percent for cost-of-living increases for federal retirees would be lifted.

A pending supplemental appropriations bill, including extended unemployment benefits and an emergency housing program that the administration opposes, would be accommodated, Michel said.

Democratic leaders also edged closer to completing their alternative, which House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said will be put into final shape today.

While offering no details, O'Neill issued a statement saying it would "put people to work in housing and youth employment and other areas" and channel money into "technological development that will stimulate economic growth and future jobs."

On the issue of the deficit, O'Neill said only that the House Democratic plan would aim for "lower deficits and lower interest rates than those resulting from the Senate-passed budget," meaning a deficit of less than the Republican-dominated Senate's projected level of $116 billion.

A showdown between the Republican and Democratic budget proposals is expected on the House floor Thursday, two weeks after a rebellious House rejected a total of eight budget alternatives, including a Republican alternative deficit that exceeded $100 billion.

"We've got to get under $100 billion. . . . It's a psychological barrier," Michel said in a cautious appraisal of the plan.

Approval of the plan by Republican leaders, who have been consulting with conservative Democrats, moderate GOP "Gypsy Moths" and more conservative Republican "Yellow Jackets," was contingent on a Congressional Budget Office review today, Michel said. Presumably, if the CBO numbers showed a deficit of more than $100 billion, further changes would be made.

It was unclear yesterday whether either the Republican or Democratic plan had enough votes for passage, although even Democrats conceded the GOP version probably had the best shot.

"I think what was going on in that Republican meeting room was a pretty cold-blooded search for votes," said Rep. Barber B. Conable (R-N.Y.) as he left the session, adding that "everyone is very nervous about whether it the proposal means anything or not."

Conable conceded that moderate Republicans might have some problems with the proposal but indicated he thought they would go along. There was no immediate comment from moderates at the meeting.

"Nobody's satisfied with anything," said Michel glumly. Asked if it could pass, he shrugged and said, "Well, it's going to be still on the margin."

In the earlier budget vote, the Republican proposal made the strongest showing but was defeated, 192 to 125. It lost the support of many GOP moderates and failed to pick up as many conservative Democrats as Republican leaders had hoped for.

Last year Reagan had the support of almost all Republicans and a large number of Democratic conservatives in congressional victories for his program of tax and budget cuts. Michel and other Republican leaders have been attempting to recreate this coalition in their latest round of budget negotiations.

House Democratic aides said the precise form of their budget plan was still unresolved and might include aspects of a "pay as you go" proposal offered last month by Rep. George Miller (D-Calif.), under which spending increases would be offset by tax increases.

They also said no decision had yet been made on whether to allow an amendment by House Appropriations Committee Chairman Jamie L. Whitten (D-Miss.) to strike out a major budget enforcement provision under which money bills that exceed budget targets cannot be passed. The House passed Whitten's amendment last month before rejecting all the budget proposals.