Alarmed that the unchecked growth of federal entitlement programs may choke off their grant pipeline from Washington, three leading governors pleaded yesterday for a three-year moratorium on further cuts of grants-in-aid.

Two Democrats and a Republican representing the National Governors Association also agreed with senators' contention that the scheduled federal income tax cuts may have to be postponed or rolled back to avert a budget crunch.

Asked by Sen. Sam Nunn (D-Ga.) if Congress had gone "too far" in cutting taxes last summer, Govs. Richard A. Snelling (R) of Vermont, George Busbee (D) of Georgia and Scott M. Matheson (D) of Utah all gave quick affirmative replies.

Sen. David F. Durenberger (R-Minn.) arranged the hearing of his intergovernmental relations subcommittee as a forum for the governors to air their complaint that continued uncertainty over the amounts of federal aid the states can expect is causing what Busbee called "disarray and chaos" in state budgeting.

Snelling said that governors would accept "level funding at about $46 billion a year for discretionary grants to state and local governments for 1983 and 1984" as a way of ending the uncertainty. That figure had been suggested in the first Reagan budget proposals last March, but more recent indications have been that the federal grants might be cut far below that level.

Snelling noted with alarm that the Congressional Budget Office had estimated in September that pressures from defense and entitlement programs' growth might leave only $8 billion available in 1984 to fund the grants for state and local governments.

Snelling also noted that the administration was budgeting an annual 8 percent increase in direct federal payments to individuals--the so-called entitlement programs, including Social Security and Medicare--but only a 4 percent increase in payments to individuals through states and localities, in programs like Medicaid and Aid to Families with Dependent Children.

He said it would be more logical to set the same cap on the growth of all such programs, which would mean trimming the federal entitlements.

Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) told Snelling he agreed, adding, "I hope the administration is listening, too."