Twenty-four Republican senators objected yesterday to the bipartisan budget approved last week by the Senate Budget Committee, and they urged in a letter to Majority Leader Robert J. Dole (R-Kan.) that it be overhauled.

The group, representing slightly less than half of the GOP's 53-member majority and coming mostly from its conservative wing, complained particularly about tax increases and defense spending constraints that the GOP-controlled panel approved in an effort to gain the votes of members of both parties.

In its $1 trillion budget plan for fiscal 1987, the committee called for tax and other revenue increases of $18.7 billion, about triple the amount recommended by President Reagan, and proposed cutting $25 billion from his defense spending request.

It agreed to increase defense spending authority by only enough to cover costs of inflation, while Reagan had sought a defense spending increase of 8 percent above inflation.

The White House has sharply criticized the proposal.

"The Senate Budget Committee's proposal, as a starting point for negotiations with the Democratic-controlled House, guarantees an unacceptable result for both defense spending and new revenues," the 24 senators told Dole in their letter.

The group, led by Sen. Dan Quayle (R-Ind.), a member of the Budget and Armed Services committees, proposed no alternative but said, "We hope that, by working with you, a more acceptable alternative can be devised."

Dole has also voiced reservations about defense and tax aspects of the budget and has postponed Senate consideration of the budget, originally scheduled this week, until after Congress returns April 7 from its recess.

Dole extended feelers for consultations with the White House, but senior presidential aides have said Reagan will not negotiate a joint White House-Senate budget, as in the past.

No specific date has been set for consideration of the budget on the Senate floor.

Dole aides said a week of further deliberations is possible before action is scheduled.

Budget Committee Chairman Pete V. Domenici (R-N.M.) said he does not think that senators can reach a compromise that will suit the group of 24 and pass the Senate.

"Considering the circumstances, I think it's a very mild letter," said Domenici, apparently referring to the controversial nature of the panel's draft.