The Democratic-controlled House, pushing aside threats of a presidential veto, voted yesterday to set up a $4 billion anti-recession program of health insurance for the unemployed.

Republicans charged that the system would wind up as a permanent item of uncontrollable spending, and complained that it would be "fiscally irresponsible" to support it since it contains no financing provisions.

The bill, approved 252 to 174, would entitle participating states to fixed amounts of federal funds, determined by a mixture of unemployment statistics, to provide health services for the jobless and their families. Those out of work for a year or more would get priority.

The House Social Security subcommittee, meanwhile, approved by voice vote a bill to ease procedures for hundreds of thousands of people threatened with removal from Social Security disability rolls.

If it becomes law, the disability measure--coupled with similar revisions already ordered administratively by Health and Human Services Secretary Margaret M. Heckler--would cost between $4.8 billion and $8.8 billion over the next five years. It would constitute one of the largest benefit increases in any social program since President Reagan took office.

The health insurance program approved by the House would not require any follow-up appropriations and would go into effect immediately if it becomes law. The grants would expire on Oct. 1, 1985.

The Senate Finance Committee has approved a $1.8 billion version, to be paid for by cutting back spending in the Medicare program for the elderly and disabled. The Senate Labor Committee has approved a somewhat different $1.8 billion measure. Sponsors hope for Senate floor action after the summer recess. The administration is insisting that any bill include self-financing provisions.

House Republicans charged that the measure approved yesterday was nothing but a "political statement" since it was unacceptable to Reagan in its present form. Democrats countered that it would be pointless to wait for Reagan to make up his mind on health insurance.

The House bill would provide $350 million in block grants to the states during the rest of the current fiscal year, $1.869 billion in fiscal 1984 and $1.538 billion in fiscal 1985.

State contributions would vary from zero to 20 percent, depending on the unemployment rate. According to preliminary estimates, the District of Columbia would be entitled to $5.9 million in the coming fiscal year, in return for 5 percent matching funds, or $300,000. Maryland would get $26.8 million in return for 12 percent matching funds, or $3.7 million. Virginia would be entitled to $26.1 million for an ante of 14 percent, or $4.2 million.

Other provisions of the House bill would:

* Require employers who provide health insurance to offer a 30-day open enrollment period for unemployed spouses of current employes and, later, to offer continued health coverage for 90 days to laid-off workers. Laid-off workers would also have the option of converting their group health insurance to individual coverage.

* Set up a new program of direct grants to hospitals that serve a "significantly disproportionate" number of low-income patients unable to pay their bills because they have no Medicare, Medicaid or private health insurance. The bill authorizes appropriations for this purpose of $96 million in fiscal 1984, $77 million in 1985 and $60 million in 1986.

Floor debate was hurried along under what GOP members assailed as a "gag rule" that sharply limited amendments. Republicans fought adoption of the rule but were defeated, 227 to 196.

As a consequence, House GOP opponents were forced to make their stand on a motion to recommit the bill by Rep. Thomas J. Tauke (R-Iowa).

Tauke proposed to cut back the program to $900 million a year for two years and tie it to the congressional appropriations process. His proposal would also have permitted the states to adopt means tests to determine eligibility. He lost, 255 to 171.

Majority Leader James C. Wright Jr. (D-Tex.) said the program would provide an average of nine hospital days and 10 physician visits for 12.7 million people in fiscal 1984 if all states participated fully. He said the GOP proposal would have provided three hospital days and three physician visits.

Democrats, led by Chairman J.J. (Jake) Pickle (D-Tex.), followed up later in the afernoon by pushing the disability bill through the Social Security subcommittee. The action came after widespread protests that the administration was removing people from the rolls without sufficient evidence or procedural care.

Under the bill, a cutback version of one offered by Rep. James M. Shannon (D-Mass.), an individual's benefits would continue until his or her appeal to an administrative law judge had been decided. The government would have to show medical improvement in most cases before removing anyone from the rolls.

In addition, the government would be urged to be more careful in judging an individual's ability to work.

The government also would be bound to apply appellate court rulings to all relevant cases in a particular circuit and not just the individual case that occasioned the ruling.

The disability bill would cost about $3.8 billion, including $1.4 billion in added administrative and Medicare benefits, over the next five years. Disability payments now total about $18 billion a year.