Key Senate Finance Committee members agreed yesterday to a compromise proposal limiting the use of tax-exempt bonds, although the package is considerably less restrictive than the bond provisions approved by the House of Representatives last year.

Other amendments are expected when the bond section of the tax-revision legislation comes up for a vote in committee Thursday, but committee Chairman Bob Packwood (R-Ore.) said he believes the bulk of the compromise package will pass. It was negotiated principally with Sen. David Durenberger (R-Minn.), although other Finance members also were involved.

Finance members also voted yesterday to tax "unearned" income generated from gifts of assets by parents to their children at the parents' tax rate, a move that would end a popular method of sheltering income. The tax plan also would repeal so-called "Clifford trusts," another method of transferring income from parent to child to reduce taxes.

Packwood originally had proposed exempting the first $5,000 of income for minor children but covering gifts from grandparents and other non-parental sources in his tax proposal. But he decided instead to accept the provision proposed by President Reagan, which would exempt the first $2,000 in interest or other nonwage income but cover only gifts from parents.

Other gifts would be taxed at the child's rate. The change, affecting about 1.5 million families, would apply to children under 14 years of age, and would raise $1.2 billion in additional tax revenue over five years.

However, an amendment proposed later by Sen. Lloyd Bentsen (D-Tex.) that would index brackets of the estate tax to inflation would cost $700 million in revenue. The sum total of the committee's actions yesterday, some raising revenue and others losing it, more or less canceled each other out. Altogether, Packwood's sweeping tax proposal is in the hole by about $14.5 billion over five years.

That five-year deficit would have increased significantly if the panel had not voted down an amendment by Sen. Steven Symms (R-Idaho) to do away with the generation-skipping transfer tax. That tax is levied on transfers from grandparents to grandchildren, to keep families from escaping the estate tax every other generation. Its repeal would have cost $5 billion.

The bond compromise concerned an issue that has been hotly lobbied by state and local governments, private business and bond dealers and lawyers. Like the House bill, it would leave untaxed the interest paid by general obligation bonds issued directly by state and municipal government.

Instead, the restrictions would apply to quasi-governmental bonds, such as those for airports, solid-waste disposal and universities, and industrial development bonds. The interest those bonds pay to investors now is tax-exempt, even though they serve a partially private purpose.

The House legislation would restrict those bonds essentially by cutting the extent of permissible private participation from 25 to 10 percent of the proceeds of an issue, and by imposing a ceiling on the total number of bonds that could be issued in each state.

The Durenberger-Packwood compromise, which is less restrictive than what Packwood originally proposed, would retain the current law's private-participation limit of 25 percent, and would take certain kinds of bonds out from under the volume cap. Among them: multifamily housing bonds and bonds for nonprofit institutions such as universities.

The Packwood plan would have lost $3.4 billion over five years, mostly because it extended two kinds of bonds that would have expired under existing law. The Durenberger compromise increased that revenue loss to $4.4 billion. The bond provisions of the House bill would raise $4.4 billion.

The compromise also created two new kinds of tax-exempt bonds: to pay for disposal of hazardous waste and to pay for certain public heating and cooling facilities. The addition of the hazardous-waste category demonstrated the political popularity of tax-exempt bonds: It was strongly supported by one of the chief Senate proponents of tax overhaul, Bill Bradley (D-N.J.).

Other amendments are expected. Sen. John Danforth (R-Mo.) said, for example, that he may propose doing away with a cap on bonds for private universities that would limit the total amount of outstanding bonds they can have to $150 million. Treasury officials said that limit affects only 15 to 20 private colleges in the United States.