House and Senate leaders yesterday jockeyed for advantage on the eve of their budget negotiations as House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) dug in his heels against Senate-proposed Social Security cutbacks and Senate Majority Leader Robert J. Dole (R-Kan.) suggested even deeper deficit reductions.

The maneuvering underscored expectations that the House-Senate conference will, as Dole put it, have a "fairly difficult" time resolving differences over spending cuts aimed at reducing deficits by half to about $100 billion over the next three years.

In a surprise move, Dole, citing what he called "scary" new projections for the economy, suggested $50 billion to $60 billion in deficit reductions that he said should be made on top of the nearly $300 billion in three-year spending cuts approved earlier by the Senate.

He said new deficit reductions, such as revenue from including state and local government employes in the Social Security system, may be necessary to offset a surge in deficits that could result from less-than-anticipated economic growth. The latest consensus estimate of private economists, contained in a summary being circulated by Office of Management and Budget Director David A. Stockman, suggests that the economic outlook is less optimistic than assumptions used by the administration in its preparation of the budget.

Based on these new projections, Stockman said the fiscal 1988 deficit would be about $175 billion, or roughly $70 billion more than projected by the Senate, even if all the Senate's cuts are approved.

But O'Neill's reiteration yesterday of opposition to the Senate's proposal for a one-year freeze on Social Security benefits underscored the difficulty the conferees will have in even matching the original House and Senate numbers.

If the Senate's proposed freeze on Social Security and other government pension benefits is dropped, the Senate's proposed savings would shrink by about $30 billion over three years in the Senate draft. And if the Senate prevails on defense spending in a trade-off between the two issues, the House package would shrink by more than $20 billion over three years. It would take a big chunk of the new cuts suggested by Dole just to meet the targets set by the two houses.

Dole's proposal to apply Social Security payroll taxes to state and municipal employes would provide nowhere near enough to make up the difference: $8.3 billion in cuts in retirement and health care programs over three years if applied to all workers hired after next Jan. 1. Moreover, it could be argued -- although Dole disputes the contention -- that this would amount to a tax increase, which the Reagan administration has opposed.

Anticipating strong House opposition to eliminating inflation adjustments for Social Security next year, Dole said yesterday that the House will have to "give us just about every other cut" if it resists any Social Security constraints. This would presumably include about $4 billion in cuts in other domestic programs that were approved by the Senate and rejected by the House. In his comments on Social Security, O'Neill said House conferees "will not agree to a cut that will force 400,000 Americans below the poverty line," adding that there will be "no deal" on Social Security.

O'Neill also defended the defense spending freeze proposed by the House, saying it is "time to take a breather in the defense buildup." Dole said willingness to compromise on the part of the Senate, which has proposed a 3 percent increase above inflation for defense, "depends on what's negotiable on [the House's] side."