With the House scheduled to vote on the Ways and Means Committee's tax-overhaul legislation in less than a week, its supporters, led by committee Chairman Dan Rostenkowski (D-Ill.), and opponents, led by a unified House Republican leadership, are scrambling to line up votes.

In the middle is the White House, which started the push for the tax-overhaul legislation but has carefully avoided embracing either the plan developed by the committee with the involvement of the Treasury Department or the alternative being crafted by the House Republican leadership.

As both sides began counting noses yesterday, Democratic leaders reiterated their claim that President Reagan must begin working his party for votes if he wants a tax bill to pass the Democratic-controlled House before Congress adjourns for the year.

House GOP leaders have predicted that fewer than 30 of the House's 182 Republicans will vote for the Ways and Means bill.

Democratic officials said yesterday that it was too early to tell how many of the House's 253 Democrats will support the committee bill, since many lawmakers are trying to determine what is in it and large groups of Democrats -- from oil-producing states, timber regions and steel-mill areas, among others -- are actively opposing it.

A complicating factor is that while House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) strongly supports the bill, House Majority Leader James C. Wright Jr. (D-Tex.) does not like the measure.

Democrats said they expect Wright to make a behind-the-scenes effort to kill the bill, but he is leery of creating the public perception of a split with O'Neill.

A task force of Ways and Means members and other key lawmakers has been meeting with groups of Democrats to explain the measure and press for their votes. And outside lobbyists supporting the Ways and Means bill, including some representing business, labor and liberal think-tanks, were given lists of House members to contact.

Meanwhile, opponents of the bill, such as the steel-area lawmakers, were negotiating with Rostenkowski for future concessions that might allow them to support the bill now.

An equally powerful coalition of lobbyists, including the U.S. Chamber of Commerce and several other potent umbrella organizations representing business, is working to defeat the committee bill.

Republicans yesterday released an updated draft of their alternative. One GOP official said the new version contains "goodies" designed to appeal to many Democrats disenchanted with the Ways and Means product.

Among other things, it offers concessions to timber, oil and gas, and steel-producing areas.

While GOP officials said the alternative is unlikely to pass, they said it is politically important for Republican lawmakers to be able to vote for something labeled tax reform.

Administration officials are putting together a list of about 20 Republicans "fence-sitters" who Reagan could contact about supporting the Ways and Means bill if GOP substitute fails.

However, administration officials say that even with active lobbying by Reagan, they will get only 40 Republican votes at the most, well shy of the 75 O'Neill and other House Democratic leaders say are necessary for passage of the committee plan. The administration officials maintain that the bill will have enough Democratic support to make 40 Republican votes sufficient.