House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) asked yesterday for a meeting with President Reagan to explain the political pressures involved in overhauling the tax code.

Responding to questions after a speech to a business group here, Rostenkowski said Reagan probably is "somewhat dismayed" at the compromises Rostenkowski has made to keep the ticklish legislation moving through his committee. "I'd like to have the opportunity to discuss that with the president," Rostenkowski said.

Reagan on Wednesday complained about "waterings-down" of the tax revision proposal the president sent to Congress, and administration officials said they were sending a signal to the Ways and Means panel that retention of too many tax breaks was limiting the committee's ability to cut the top tax rate to 35 percent, as Reagan has proposed. Rostenkowski's response, in the speech and later, was that compromise is an essential part of tax legislation and Reagan should learn that.

"I'd like to invite him to the lobby of the Ways and Means Committee, have him walk through -- if he can -- the groups that are outside while we're negotiating inside the committee," Rostenkowski said.

The halls outside room 1100 of the Longworth Building have been packed with lobbyists of all persuasions every day the committee has debated the tax measure, which would curb tax preferences that such interest groups as manufacturing industries, insurance firms, charities, universities and real estate concerns consider vital.

As he did during a similar speech in Chicago Thursday, Rostenkowski complained that tax overhaul is getting less support from committee Republicans than it is from Democrats. That alignment is not expected to change if the measure makes its way to the Senate, where 22 Republicans are up for reelection in 1986.

Senate Finance Committee Chairman Bob Packwood (R-Ore.) also has doubts about some elements of tax overhaul, including removal of several tax benefits for timber, a home-state industry.

"The president controls the Senate," Rostenkowski said. "I'm sure he can go over to the Senate and, with his magnetic, magnificent personality, induce Packwood to treat timber like we should treat timber, and talk to Senate Majority Leader Robert J. Dole R-Kan. about farms and wheat. My solace is that the president can work with the Senate."

At another point in his speech, Rostenkowski said he doubted the Senate could enact a tax-overhaul bill, saying that anyone should be "surprised as heck if they get a bill out of the Senate." With all those GOP senators running for reelection, he said, "I suggest they'd be awfully nervous about visiting the tax code."

Rostenkowski also implied that, if he had it to do again, he would think twice about allying himself with a Republican president for a cause with questionable public support.

"I'll never jump on the bandwagon again as soon as I have," he said. "I'm at war every day, from one foxhole to the next."