The Reagan administration's handpicked federalism advisory committee met for the first time yesterday and promptly ran into the same kind of money and turf conflicts between state and local officials that have beset previous efforts in this field.

When President Reagan named the group on April 8 in order to "help me restore a proper constitutional relationship between the federal, state and local governments," it seemed tailor-made as a ratifying device for his current and promised proposals to divest Washington or responsibility for many domestic programs.

Its chairman was the president's good friend, Sen. Paul Laxalt (R-Nev.). Twenty-two of the 34 elected officials and all five of the private citizens named to serve on the committee were Republicans, and many of the Democrats were southern and western conservatives.

Yesterday's session was launched on a high note with Laxalt, Richard S. Williamson, Reagan's assistant for intergovernmental relations, and F. Clifton White, the veteran conservative political organizer who suggested the committee to Reagan, all declaring that after decades of talk the moment had arrived for what White called "a new revolution" in the federal system.

But when Tennessee Gov. Lamar Alexander, a Republican, urged the conferees to "get to specifics quickly," the same thorny problems appeared that have the beset Reagan's proposals to Congress for converting dozens of narrow categorical federal aid programs into block grants to states and localities.

Bruce K. Nestende, an Orange County, Calif., supervisor and former aide to Reagan in California, said that Congress had to guarantee "local input" in state block grant allocations, "or else they'll just peel off the money for their own purposes."

Laxalt said he had heard many such comments about the pending block grant proposals, observing: "A lot of people view state government with more alarm than they do Washington. I find it hard to believe, but it's true."

Indianapolis Mayor William H. Hudnut III, a Republican and current president of the U.S. League of Cities, said he fellow mayors would be unhappy if the Reagan version of federalism simply transformed the cities from "administrative provinces of the federal government to administrative provinces of the states."

Georgia Gov. George yd. Busbee, the chairman of the National Governors Association, said the Georgia Municipal League "likes this [block grant] program, despite what the lobbyists in Washington and [Atlanta Mayor] Maynard Jackson say." But Busbee, a Democrat, expressed his own concern that Reagan was asking the states to absorb a 25 percent cut in grant funds, rather than the 10 percent reduction the governors had told him they could accept in return for the added flexibility of the block grants.

The administration trotted out five Cabinet members -- Richard S. Schweiker of Health and Human Services, Drew L. Lewis of Transportation, James G. Watt of Interior, Samuel R. Pierce Jr. of Housing and Urban Development and Terrel H. Bell of Education -- to talk about the federalism initiatives in their areas.

But the sniping between the spokesman for other levels of government continued unabated. Vermont Gov. Richard A. Snelling, a Republican, told Lewis it would be a mistake to give cities any portion of the highway money because states need it all to "equalize economic opportunities." County Executive William J. Murphy of Troy, N.Y., a Republican, complained bitterly about Lewis' decision to cut back operating subsidies for mass transit systems and said, "State government has paid little or no heed to the goals and aspirations of local governments." Lewis suggested that maybe Snelling and Murphy could work out the argument between themselves.

Phoenix Mayor Margaret Hance, a Republican, seemed to capsulize the suspicions of those who have been through these fights before, when she said, in an apparent reference to White's suggestion that the Reagan "revolution" required most of all a change in attitude: "We're told to go to the state. We're told to have a happy attitude. But happy attitudes in the past have not buttered our parsnips."

When the committee called on Reagan in the White Reagan yesterday afternoon, the president put a better face on things. "It's going to be hard to convince Washington that the people of this country want these responsibilities back," he said. "But I'm going to fight it out if it takes all summer and then some."