President Reagan's tax-simplification proposal received its first public airing on Capitol Hill yesterday, with House Ways and Means Committee members quickly challenging several key provisions while forcing the administration to hedge on its prediction that the far-reaching revision would increase economic growth.

Members of the tax-writing committee, which gets first shot at all major revenue-raising legislation, generally praised the broad outlines of the simplification plan. But, in a preview of the obstacles that lie ahead, they criticized Treasury Secretary James A. Baker III for such proposals as eliminating the federal tax deduction for state and local income taxes and tightening business depreciation writeoffs and for its treatment of the oil and gas industry.

While the committee was taking its first day of testimony, Reagan traveled to Williamsburg, Va., and Oshkosh, Wis., to sell the plan to "Main Street America" as a tax cut and a rebellion against "oppressive" government taxation.

With hundreds of lobbyists and reporters filling the ornate Ways and Means Committee room, members made clear within two hours that repeal of the deduction for state and local taxes is the least popular provision. However, because it is the single largest source of revenue needed to offset lower tax rates in the Reagan plan, it is the provision on which administration officials are least willing to compromise.

Other tax advantages that emerged as possible sticking points include taxation of the buildup in value of whole-life insurance policies and limitations on mortgage interest deductions for second homes.

Underlying the debate was the broader question of whether the proposed tax cut for the rich would be too great and the cut for the middle class too small.

Committee Chairman Dan Rostenkowski (D-Ill.) was one of the strongest supporters of the president's proposal, calling it "monumental." In his first comment on the substance of the plan, Rostenkowski said it "generally holds to the sturdy principles of fairness and simplicity."

But Rostenkowski criticized the plan for a projected loss of $12 billion in federal tax revenue from 1986 to 1990, noting that the Treasury Department's original plan would have gained that amount. Both Reagan and Rostenkowski are aiming for "revenue-neutrality," keeping total federal income unchanged by lowering rates while curtailing various deductions and credits.

In his first appearance to promote the plan, Baker said the $12 billion estimate represents 0.24 percent of estimated federal receipts over the period, well within the margin of error of Treasury's estimates.

But Baker had a more difficult time detailing projections that the plan would increase gross national product by 1.5 percent by 1995 and lower the cost of capital -- the interest and tax costs of obtaining funds -- by 20 percent.

In response to repeated questions about how those figure were derived, Baker said he would release the econometric model behind the predictions in three weeks, after more testing is done.

"While we've done this in the past, we haven't always done it right at the start," he said.

It became apparent early in the hearing that most of the questions would concern pet provisions of each member. Of the first three questioners, two asked Baker about taxation of increases in insurance-policy value.

Other questions concerned repealing the deduction for families with two incomes, the "marriage penalty," limiting interest deductions for mortgages on second homes and terminating the 10 percent investment tax credit. Baker was criticized both for restoring loopholes and for axing loopholes.

By lunchtime, the committee was discussing such esoteric matters as accrual accounting for row crops in Calfornia and depreciation for solar- and wind-power devices, both concerns of Rep. William M. Thomas (R-Calif.).

In between, the most common complaint of committee members was the proposed termination of state and local tax deductions, which would raise $34 billion a year and which the administration contends is a subsidy for taxpayers in high-tax states.

Legislators were particularly peeved that the administration offered no compromises on that provision, while restoring several tax advantages to the oil and gas industry that would have been eliminated in the original Treasury plan.

"I don't see why the taxpayers of Massachusetts should subsidize the oil and gas industry if they can't deduct state and local taxes," said Rep. Brian J. Donnelly (D-Mass.).

Several committee members charged that Baker had produced a 461-page proposal that in many cases would make the tax code even more complicated.