A bipartisan Senate negotiating team proposed a "hardball" budget compromise yesterday that would force President Reagan and Congress to accept tax increases as the price for additional spending for defense and other sensitive programs.

House bargainers expressed interest as well as misgivings and agreed to respond Monday.

In unveiling the plan, Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) made it clear that Senate Republicans had given up hope of talking the president into voluntarily accepting tax increases to help meet the Gramm-Rudman-Hollings deficit target of $144 billion for fiscal 1987.

"I don't believe this proposal requires support from the president," he said. "If we want to play some hardball, that's our prerogative."

As outlined by Domenici and Sen. Lawton Chiles (Fla.), ranking Democrat on the committee, the plan would create a $7.3 billion "reserve revenue fund" that could be used for defense ($3 billion) and other programs including embassy security ($100 million), space shuttle repairs ($400 million) and a potpourri of domestic programs totaling $3.4 billion.

The domestic programs include farm credit relief, education, job training, health, trade promotion and other ventures dear to the hearts of the Democratic majority in the House.

But the money could be tapped only if Congress approves, and Reagan signs, a bill raising taxes by $7.3 billion, or $47 billion over three years. Congress could not allocate the extra money until it passes the tax bill, and Reagan could not spend it until he signs the tax measure.

"A leveraged buyout -- there's a little leverage on everyone," Chiles said. "A poison pill for all of us," added Domenici.

House Democrats expressed reservations on several grounds, principally the effect of a presidential veto of the tax bill on domestic expenditures included in their budget. "I think there's a problem getting votes to override a presidential veto , but it's an interesting offer," said House Budget Committee Chairman William H. Gray III (D-Pa.).

Gray pressed Domenici on whether the plan has the backing of the Senate Republican leadership and might get the necessary two-thirds vote on a veto-override attempt.

Domenici said he cannot believe Senate Majority Leader Robert J. Dole (R-Kan.) would be "anything but supportive" and added enigmatically, "There are just an awful lot of ways to skin a cat. I believe it will be enacted into law if it is passed in this form."

Domenici refused to elaborate on the cat-skinning remark, but others have speculated that the tax increase may be tied in some way to the tax-overhaul bill, which Reagan strongly supports.

Also, under the Senate's new offer, the Pentagon would be faced with a defense budget that does no more than split the difference between House and Senate numbers, providing $293 billion in long-term spending authority and $279 billion in actual outlays for the year, unless the reserve fund is approved. This would not be enough to keep pace with inflation under current estimates. The reserve would bring the defense allocations within range of what the Senate approved earlier this year.

Moreover, the Senate proposal does nothing to meet objections about the gap between spending authority and outlays, casting doubt over whether defense appropriations could reach even as high as $293 billion and still come within the Gramm-Rudman-Hollings outlay restrictions. Gray suggested that a spending authority figure of $288 billion would be more appropriate.

The White House had no immediate comment, although yesterday Reagan repeated his opposition to tax increases, saying spending should be cut first. But in remarks to a group of editors and publishers, he also said that military spending should not be cut because "defense is the first priority . . . of the federal government" under the Constitution.