The Carter Administration moved yesterday toward a possible compromise with Rep. Jack Brooks (D-Tex.) on the terms of the President's authority to reorganize the government.

With a markup session on the reorganization authority bill scheduled for today in a House Government Operations subcommittee, Brooks, chairman of the full committee, backed off his previous adamant opposition to the President's proposal.

The Senate has already approved Carter's request for authority to reorganize subcabinet agencies by submitting plans to Congress that take effect automatically unless vetoed within 60 days by the House or Senate.

Brooks objected that the "legislative veto" mechanism was unconstitutional and pushed for an alternative bill that would require an affirmative vote by both the House and Senate for a reorganization plan to become effective.

But with a near-majority of his committee backing the Carter approach, the Texas Democrat yesterday made public a compromise proposal he had been discussing for several days with committee members who favored the Carter bill.

Under its terms, Carter preserves his basic goal of having reorganization plans take effect unless voted down by the House or Senate, even though Brooks said, "I still believe the legislative veto is unconstitutional."

But the compromise picks up a proposal from Brooks' bill making it easier to get a floor vote on each reorganization plan.

The Brooks compromise contains two other restrictions on the braod authority Carter has been seeking. it would limit each reorganization plan to "one logically consistent subject matter," and prevent the President from having more than three plans pending before Congress at any time.

Carter wanted no limit on the content or the frequency of his reorganization plans. The Senate restricted the subject matter along the lines of Brooks' proposal but accepted assurances from the administration that it would not "inundate" Congress with plans, without putting a specific numerical limit into the bill.

Brooks said he had been told the administration was sympathetic to his compromise, but that was not immediately confirmed by the White Houe.

Pro-Carter members of Brooks's committee are urging the compromise, saying the President would be better to accept some limitation on his authority rather than running the risk of antagonizing Brooks by defeating him on a straight test of strength.