House Republican leaders yesterday delivered to President Reagan a letter signed by 146 members showing that he has the votes to sustain his threatened vetoes the rest of this year of spending bills he considers excessive.

The pledge was made by 144 Republicans and two Democrats who recommended vetoes of specific new programs to avert what they described as a "massive increase" in spending.

The spending issues, meanwhile, continued to preoccupy both houses of Congress.

The House, by 263 to 158, approved and sent to the Senate a much-trimmed $15.6 billion housing authorization bill. It would put the government back in production of housing for the poor but otherwise provide little more than what backers called "life-support" for federal programs. Details on Page A6

* The Senate Finance Committee reported out, 11 to 4, a bill providing $1.8 billion over the next 2 1/2 years in grants to the states for health insurance for the unemployed. But the committee also approved cuts in existing programs to pay for the new program.

The letter supporting Reagan's veto threat expressed "alarm" about a "massive increase in spending" that could "reverse our progress on interest rates and choke off the economic recovery . . . . "

The congressmen urged Reagan to veto the housing bill the House passed yesterday on grounds it would not curtail "uncontrolled growth" of future housing assistance costs. They also urged vetoes of two Democratic-sponsored recession relief bills, one to aid the unemployed meet mortgage payments, the other to expand public works to provide new jobs. And they called on the president to veto any bill providing health benefits to the unemployed unless it is accompanied by some financing provision.

Rep. Phil Gramm (R-Tex.) said Reagan could save about $40 billion in spending authority over three years if he followed this advice and also vetoed appropriations bills over his requests.

The letter was welcomed at the White House as further ammunition for Reagan's planned veto confrontation with Congress later this summer. Reagan has warned repeatedly that he will veto "budget-busting" money bills, setting the stage for a likely partisan showdown with Democrats going into the 1984 campaign.

The two Democrats who signed the letter were Dan Daniel (Va.) and Larry McDonald (Ga.)

Before approving the health insurance bill, the Senate Finance Committee adopted an amendment by Chairman Robert J. Dole (R-Kan.) to finance the cost of the new program by increases in the currently scheduled premiums patients pay for the doctor bill part of Medicare, and by freezing for nine months the fees that Medicare pays participating physicians.

These provisions would cover the basic cost of the insurance program, which President Reagan has set as a condition for his approval.

In another amendment, sponsored by John C. Danforth (R-Mo.), the committee voted to require the states to impose a means test on unemployed workers seeking aid. Under the Danforth amendment no worker could receive help if his family income exceeded the median for families of similar size in his state.

In the final 11-to-4 vote, Democrats Max Baucus (Mont.) and Bill Bradley (N. J.) opposed the bill and were joined by conservatives Malcolm Wallop (R-Wyo.) and Steve Symms (R-Idaho). Eight Republicans and three Democrats voted for it.

Under the bill states could require workers to pay part of the cost of the new health insurance.

The House Ways and Means Committee, in conjunction with leading members of the House Energy Committee, has approved a rival bill providing $4 billion over the next 2 1/2 years for health insurance for the unemployed. The Senate Labor Committee also has approved a bill providing $1.8 billion over the next 2 1/2 years. Neither of those measures include a means test or cuts in other programs to help offset their costs.