The Republican-controlled Senate yesterday topped the Democratic-controlled House in the amount it proposes to spend for jobs and recession relief as it also struggled to break a stalemate over a banking-industry effort to repeal the withholding of taxes on interest and dividends.

Running the risk of a presidential veto, the Senate added $1.2 billion for revenue-sharing with local governments and $100 million for health-care services to its jobs bill, increasing the cost of the anti-recession portion of the bill to more than $5 billion.

The House earlier this month approved a $4.9 billion anti-recession bill, and the Reagan administration had been relying on the Senate to pare down that bill, not expand it.

President Reagan has said, in effect, "Watch out. Don't let the bill get too big," an administration official said yesterday, adding, "There is a potential problem, yes, that the bill would get too big for the president to sign."

The revenue-sharing money, which was proposed by Sen. John Heinz (R-Pa.), is a one-time windfall that would give localities a double installment of funds this spring by accelerating payments from the end of each quarter of the year to the beginning of each quarter, was approved 73 to 21.

The extra health care money, proposed by Sen. Thomas F. Eagleton (D-Mo.), had been included in more costly form in a Democratic package of add-ons that was defeated last week. It was approved yesterday 80 to 14.

Although the Senate remained in a procedural quagmire because of a proposal by Sen. Robert W. Kasten Jr. (R-Wis.) to amend the jobs bill to repeal tax withholding for interest and dividends, there were two bright spots:

* It now appears that the jobs bill, which also includes $5 billion to continue payment of unemployment benefits, does not have to be passed until the end of the week.

The Labor Department, which had said earlier that payment of jobless benefits could not be assured after today in 27 states and the District of Columbia, said it has come up with $196.6 million to assure benefit payments at least through Friday. The money became available because states are spending less than anticipated on benefits this month, officials said.

* There was at least some talk of a compromise in the Senate that would give Kasten a vote on the withholding issue without tying it to the jobs bill or to the Social Security rescue plan that the Senate plans to take up immediately after it finishes consideration of the jobs legislation.

After a third day of wrangling among his Republican troops on the issue, a clearly frustrated Majority Leader Howard H. Baker Jr. (R-Tenn.) urged that Kasten abandon his attempt to tie withholding repeal to the jobs bill and agree to a "free-standing" vote on withholding after the Easter recess at the end of the month.

"I am determined to pass this jobs bill," Baker said.

Senate Finance Committee Chairman Robert J. Dole (R-Kan.), who has filibustered to avoid a vote on Kasten's proposal, agreed that a vote on the issue now appears inevitable but indicated he would also oppose giving Kasten a vote on withholding in connection with Social Security.

And Dole continued to pound on the banking industry for pushing for repeal of withholding, under which 10 percent of an individual's income from interest and dividends will be withheld for tax purposes starting July 1.

"There's a question of the truly needy and the truly greedy, and we ought to move on to take care of the truly needy," said Dole in urging that the jobs bill be passed without Kasten's withholding rider.

Kasten told reporters late yesterday that the Senate leadership, in consultation with House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.), would try to work out by today some kind of a legislative "vehicle" for his repeal proposal, either before or after the recess.

"One way or another we're going to force a vote on this issue," said Kasten, claiming support of "close to 70" of the 100 senators and "at least two-thirds of the House."

As of late yesterday, it was not clear what the "vehicle" might be. Reagan, who opposes repeal of the withholding provision, has vowed to veto any legislation that includes it.

Kasten, arguing that withholding will cost the economy more than the roughly $4 billion a year it is supposed to produce in tax revenues, is insisting on a vote as soon as possible so that banks and other affected corporations won't have to begin installing expensive machinery to handle the paperwork.

But he indicated yesterday that he might agree to delay a vote until after Easter, especially if he can get one without threat of a renewed filibuster by Dole.

The theatrical highlight of the day came when Dole and Kasten, both brandishing cloture petitions in their outstretched arms, tried to out-shout each other for the attention of the Senate's presiding officer.

Dole was recognized first, meaning the Senate will vote first on his motion to cut off debate on the entire bill, which could make it more difficult for Kasten to get a vote on his withholding repeal proposal.

Kasten eventually also got in his cloture petition, which would have the effect of limiting Dole's filibuster against the withholding rider.

Both debate-limiting votes are scheduled for Wednesday.