Congress officially started work on the Reagan administration tax bill yesterday with Democrats on the House Ways and Means Committee ridiculing as "jelly bean talk" and "hallucinogenic" the economic improvements the administration claims its proposal will bring.

They also demanded to know how much the administration's promised second tax bill, which would include such tax cut favorites as tuition tax credits and elimination of the so-called marriage penalty, would cost. Treasury Secretary Donald T. Regan testified he "had no idea."

Committee Chairman Dan Rostenkowski (D-Ill.) promised that the final tax bill would be "our product," indicating that there would be amendments to Reagan's proposed 30 percent cut in individual income tax rates over three years, and big business tax cuts.

The tax bill should not be passed before spending cuts, Rostenkowski also said. He refused to say how the two should be linked, and he opposes tying the tax bill directly to spending through the congressional budget process, but sources said that there were several ways to keep the tax bill off the House floor until spending was cut.

Meanwhile, Republican and Democratic leaders of the Senate Budget Committee introduced the legislative vehicle by which Reagan will try to save $125.9 billion in federal outlays over the next three years, including $41.4 billion in fiscal 1982.

But both Committee Chairman Pete V. Domenici (R-N.M.) and Sen. Ernest F. Hollings (D-S.C.), the committee's ranking minority member, warned that changes will be made in Reagan's budget-cutting program.

"In a few areas, such as child nutrition," Hollings said, "the president may achieve false economies by taking a short-term budget cut that ends up costing this nation more in both human and monetary terms over the long run."

The Domenici-Hollings resolution was referred to the Budget Committee, which will prepare instructions for specific savings to be achieved later through program cuts by authorizing committees. Domenici wants these cuts enacted by June 30, but the Democratic-controlled House, working at a more deliberate pace, anticipates taking until the August congressional recess.

In an angry exchange in Ways and Means, Regan was told the administration's economic assumptions were "hallucinogenic" by Rep. Thomas J. Downey (D-N.Y.). Regan, clearly shaken, retorted: "I resent that . . . to call the Treasury secretary of America . . ." but was interrupted as Downey said, "You cannot cite one statisitc, one report, one shred of evidence" for the assertion that the economy will take off as people save and invest their tax cuts.

Earlier Rep. J. J. Pickle (D-Tex.) said it was "jelly bean talk" to say that people would save and invest much more if the administration's tax proposals were enacted.

Reagan officials argue that the economy will rebound, as inflation falls, if Congress passes the president's economic program. But House Democrats and some Republicans are uneasy about the "new economics" underlying the administration's figures. They believe that tax cuts of the size proposed by Reagan could be inflationary; some also worry that the tax cuts would commit them to future deficit-reducing spending cuts they may not want to make. In addition, some Democrats want to give more of tax cut to the poor and less to the well-off.

Regan maintained that the rate cuts proposed by the administration could spur $70 billion of extra savings. He also told the panel that investment, which historically has been around 10 percent of the total economy, should rise to 15 percent or 18 percent of gross national product.

Private economists are skeptical of the administration's forecast that invetment will rise at 11 percent a year, after allowing for inflation. Regan floundered somewhat when asked to explain how this forecast was reached, but said that critics were "exaggerating."

Many economists doubt the administration view that tax cuts will make people work harder."Isn't it more likely," Pickle asked Regan yesterday, "that the eager beaver will continue to work hard, and the laid-back folks will continue to lay back?"

The Treasury secretary's refusal to give any estimate of how much a second tax bill would cost, and how it would be paid for, led one congressman to remark that the proposed Reagan budget "doesn't leave room for Mr. Regan's second tax bill."

Reagan eventually said that the first tax bill would stimulate the economy so much that there would be "plenty of room" for more tax cuts. But this assumes that the administration itself is being too pessimistic about its forecasts of the effect of its tax proposals.

Budget director David A. Stockman also came in for some fierce questioning yesterday. Asked about how the poor would be hit by proposed budget cuts, he said all the cuts would "cause some people to believe that they've been adversely impacted." Rep. Charles B. Rangel (D-N.Y.) shot back that it was not just a matter of belief, if a person lost a government-sponsored job he or she truly would be affected.

Stockman also rejected the "notion" of tax expenditures, whereby some credits and deductions against tax are considered a kind of spending by the government, when he was asked whether closing loopholes, or tightening up on special credits and deductions, would be one way to raise revenue for the second tax bill. But later he admitted that some tax credits, such as the tuition tax credit which Reagan suggested for the second tax bill, can be looked at as a kind of spending outlay.

Tax expenditures were "the last defense mechanism" of the over burdened taxpayer, Stockman said.