The Democratic-dominated House Ways and Means Committee rejected President Reagan's proposed three-year tax cut yesterday in favor of a two-year alternative that the president, on a visit to the friendlier Republican side of the Capitol, quickly labeled a "wolf in sheep's clothing.

Reagan, gearing up for a House floor fight later this month, sharply attacked the Democratic bill as "make-believe . . . they [the Democrats] offer the mirage of tax reduction while working to lock in a tax increase. Well it won't work . . . the American people won't be fooled."

The Ways and Means Committee, which is expected to complete action later this week, approved two years of individual rate cuts tilted toward those in the middle and lower income brackets. The vote was 22 to 13, with the panel split along partisan lines except for Rep. Kent Hance, a conservative Texas Democrat who defected to the administration early in the fight and is now a principal sponsor of GOP alternative bill.

Continuing what has become a public relations contest conducted before television cameras, Rep. Dan Rostenkowski (D-Ill.), chairman of the Ways and Means Committee, contended that he and other Democrats are unwilling to back a third year of individual cuts until they are sure such reductions will not unbalance the 1984 budget.

Reflecting a new-found Democratic concern for deficit reduction, Rostenkowski said, "Until such time as this member sees where these [promised but unspecified future budget] cuts are going to be made, this member is apprehensive" about making a third year of tax reductions.

The crux of the GOP argument is that a 25 percent three-year individual rate cut is essential if taxpayers are to be able to keep pace with anticipated inflation. "The bottom line is that our bill reduces taxes in words and deeds, while theirs deals in make-believe," the president said.

The House Democrats contend, however, that the president's across-the-board cuts, the same percentage cuts for each tax bracket, in fact give disproportionate relief to the rich. This is partly because, for the better off, the Reagan cuts would more than offset already scheduled Social Security tax increases plus the effect of inflation in lifting taxpayers into higher brackets. Many households in the middle and lower brackets, however, would find their total tax bills rising.

In a related development, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) moved to counter charges of a Democratic stall on the tax bill by holding out the possiblity of enactment of the legislation before the start of the August recess.

O'Neill said that he and Senate Democratic leaders have agreed to do "everything we can to get the tax bill on the president's desk by the August recess," including the possiblity of holding Congress in session during part of the first week of August.

The Democratic bill approved yesterday provides for 15 percent rate cuts in two steps, five percent on Oct. 1, 1981, and 10 percent on July 1, 1982. These cuts would be skewed to benefit those making less than $50,000 a year.

In addition to targeting the cuts, the Democratic bill gives larger reductions to persons in lower income brackets by increasing the so-called zero bracket amount or tax threshhold, and by raising from $10,000 to $12,000 the cutoff point below which workers are eligible for the earned income credit. Neither provision is in the Republican bill.

Reagan had lunch with Republican senators to fire them up for the floor action on the tax bill on their side of the Capitol which is scheduled to start today. The Republicans are pushing the tax bill on the Senate side in part to apply pressure to the House Democrats.

In another aspect of Yesterday's maneuvering, White House spokesman David Gergen said the president does not have the votes now to prevail on taxes in the House, but expects to have them by the time the bill hits the floor.