Conservative as well as liberal Republicans joined Democrats yesterday in voicing objections to specific aspects of President Reagan's budget for next year as administration officials defended proposed spending cuts as essential to continued economic growth.

Criticism of the budget from GOP members of the Senate Appropriations Committee came as House Budget Committee Chairman William H. Gray III (D-Pa.) warned that Congress may hit "gridlock" over the budget unless Reagan takes the initiative in working out compromises on critical issues.

Though Congress wants to cut spending to reduce deficits, specific decisions are difficult to make "when the president has literally left the playing field . . . when the Gipper has gone to the skybox to await the outcome," Gray said in a speech to the National Press Club.

At the Senate committee hearing, Republicans ranging from conservative James A. McClure of Idaho to liberal Lowell P. Weicker Jr. of Connecticut characterized the proposed fiscal 1986 budget as deficient on a broad range of points.

In response to administration contentions that a constitutional amendment to require balanced budgets would provide greater "political will" to check spending, Weicker glowered at the administration witnesses and said coldly:

"I don't want any lecture on political courage. The only courage in this budget comes down on the weaker in our society."

Office of Management and Budget Director David A. Stockman, appearing before the panel with Treasury Secretary James A. Baker III and economic adviser William A. Niskanen, avoided the kind of controversial remarks that got him into trouble over the last couple of weeks, including comments on farmers' financial practices, which drew a dissent even from his mother, Carol Stockman.

At the end of the hearing, Appropriations Committee Chairman Mark O. Hatfield (R-Ore.) read a schedule of future hearings and announced, deadpan, that the committee would hear testimony from Carol Stockman on "federal budgeting and child disobedience."

"I'll tell you, I wouldn't want you back in South Dakota with me this weekend," Sen. James Abdnor (R-S.D.) said to Stockman.