The House Energy and Commerce Committee yesterday brushed aside objections from the administration and National Governors' Association and approved, 34 to 8, a bill to create a new program of health insurance for the unemployed.

The administration objects that it would create a costly new national entitlement program, in which spending would be automatic each year for all who qualified; next fiscal years' estimated federal cost would be $2.7 billion. The governors object because it would also force them to come up with matching money.

But the committee was unimpressed, and seven of the 15 Republicans joined all 27 Democrats in voting to send the measure to the floor.

There are more than 11 million unemployed now, many of whom lost their health insurance when they lost their jobs. Rep. Henry A. Waxman (D-Calif.), chairman of Energy and Commerce's health subcommittee, said he did not think President Reagan "would have the nerve" to veto the bill if it reaches him.

Rep. Edward R. Madigan (R-ILL.), ranking Republican on the health subcommittee, joined Waxman in supporting the legislation, which he called an "effort to reach out" to working people "who have paid their taxes for years" but are now without means. Workers would have to pay 2 percent of their unemployment benefits toward the cost of the coverage.

The health insurance bill is the fourth and in some ways most elaborate anti-recession proposal to move in the Democratic House this year.

The president signed the first -- a jobs bill -- but is fighting in the Senate to block farm credit and mortgage bailout bills the House also passed.

The administration has said it favors a health insurance bill, but only if it can be financed without an increase in the deficit.

The Senate, in its just-passed budget resolution, took a middle position, allowing $900 million for any new program of health insurance next year.

The House bill would authorize the new program for three years. Before approving it the committee voted 21 to 18 for an amendment by Thomas J. Bliley Jr. (R-Va.) barring abortions under the program except where the life of the mother would be endangered by continued pregnancy.

The governors say that the states cannot afford the matching money the bill would require, especially the states hardest hit by unemployment. But a substitute bill without the matching funds provision was offered by Rep. Thomas J. Tauke (R-Iowa) and lost, 27 to 15.

Under the bill, any state with unemployment of 6 percent or more -- virtually all at present -- could opt to participate in the new program. If it chose, it could limit benefits to areas within its borders with extra-high unemployment. And under a last-minute Waxman amendment, states with less than 6 percent unemployment could also opt in for their high-unemployment areas.

The federal government would reimburse the states for anywhere from 50 percent to 100 percent of program costs, depending on their unemployment rates. Within the coverage areas unemployed workers and their dependents would be eligible for aid if they were receiving unemployment insurance (or had received it during the previous two years and remained out of work) and lacked either private health insurance or Medicaid.

To obtain coverage, the worker would have to pay a premium equal to 2 percent of his weekly unemployment benefit (the state could raise this as high as 5 percent if it chose). Minimum benefits would be nine days of hospital care and 10 doctor visits per person, plus pregnancy and birth services.

In separate provisions, the bill would provide grants of $30 million in fiscal 1984 (rising to $60 million by 1986) to hospitals in high-unemployment areas that serve low-income people and would require employers to keep a laid-off person's group health benefits in effect for three months after he or she left, effective Oct. 1, 1985.