As the Senate struggled with yet another debt-ceiling increase, Finance Committee Chairman Robert J. Dole (R-Kan.) yesterday proposed a $120 billion three-year package of deficit reductions that would give the president temporary, limited powers to cut spending and raise taxes.

His proposal was unveiled shortly before the Senate rebelled against a record increase of $225.6 billion to raise the debt limit to $1.61 trillion, voting instead by a 70-to-15 margin to raise it to $1.45 trillion, enough to last about 60 days.

That limit, proposed by Sen. William L. Armstrong (R-Colo.) to increase "bargaining power" for deficit reductions, also increases chances that the debt measure, which must be passed by next Monday to avoid disruptions in government financing activities, may bog down. If it stays in the bill, the legislation will have to go back to the House, which is notoriously skittish about debt-ceiling increases.

Although Senate leadership sources have expressed skepticism about chances for Dole's measure, Dole said he has been encouraged by his colleagues' response and announced that the committee would meet today and perhaps Saturday to finish action on the proposal.

"I can't say people are jumping with joy, but there's been a very positive response . . . . It's large enough to make a difference," said Dole at a news conference to unveil the plan.

Its most unusual feature is a trade-off that would empower the president to withhold up to 2.5 percent of appropriated funds each year if similar retrenchments also were made in automatic inflation adjustments for taxes and for government pensions, including Social Security. These retrenchments would increase tax collections while cutting benefit costs.

The presidential actions could be overturned by what Dole called a "fast-track disapproval resolution," but, because the president would presumably veto a disapproval resolution, it would in effect take a two-thirds vote of both houses to override a presidential decision.

The new presidential grant of authority would take effect after next year's elections to avoid involvement in the campaign, Dole said. It would last for two years, reducing deficits now estimated at about $200 billion a year to $154 billion in 1984 and $132 billion in 1985. In all, taxes would be raised through 1986 by $56 billion and spending would be cut by $64 billion.

The budget approved by Congress earlier this year called for $73 billion in tax increases and $12.3 billion in spending cuts through fiscal 1986, and only about $10 billion is considered a sure bet now. Dole balked at the plan, saying it was tilted too heavily toward tax increases.

But Sen. Lawton E. Chiles (D-Fla.), ranking Democrat on the Budget Committee, has not given up on the budget proposals. He served notice yesterday that he will attempt to amend the proposed debt-ceiling legislation to make the increase contingent on committee approval of the budget proposals by Nov. 21 and final congressional action by Dec. 21. This would mean that Dole's committee would have to come up with $73 billion in new taxes.

In his proposal, Dole appeared to be luring President Reagan with a modified version of the "line-item" budget veto he wants, while appealing to conservatives with the prospect of holding down benefit costs and to liberals with a chance to whittle away at income tax indexation.

But he did not claim the support of Reagan, or of any senators except those who joined him at the news conference: David L. Boren (D-Okla.), John C. Danforth (R-Mo.) and Malcolm Wallop (R-Wyo.).