House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) yesterday called "on the grounds of fairness" for a cap limiting this year's income tax cut to a maximum of $700 per return, and President Reagan promptly promised to "give him my autograph on a veto."

The cut is now scheduled to be 10 percent for everyone. For those in the highest brackets this would amount to much more than $700. Democrats said that, under O'Neill's proposal, which would add $6 billion to revenues next year and slightly more thereafter, families of four with incomes up to about $50,000 would still get 10 percent; the $700 cap would start pinching only above that point.

Senate Republican leaders quickly joined Reagan in opposing the O'Neill idea.

Majority Leader Howard H. Baker Jr. (R-Tenn.) predicted that the GOP-controlled Senate would reject any change in the across-the-board cut scheduled to take effect next month.

Finance Committee Chairman Robert J. Dole (R-Kan.) said, "the third year of Reagan's three-year tax cut program is the safest bet in town." Baker, however, said he thought the Senate vote would be "close . . . , a tough fight."

O'Neill was joined in his push for the cap by Senate Minority Leader Robert C. Byrd (D-W.Va.), who set the stage for the tax vote last month, demanding it in exchange for Democratic support of administration-sponsored legislation raising the federal debt ceiling.

"We simply want to introduce fairness to the president's tax plan," Byrd said, adding that Senate Democrats are "virtually unanimous" in support of capping the tax cut in order to limit its benefits to lower- and middle-income taxpayers.

The Democratic leaders launched their assault on the third installment of Reagan's tax cut program as Congress, fresh from its Memorial Day recess, faced a jammed agenda of major tax and spending issues, including a difficult House-Senate conference on next year's budget resolution.

The budget conference is expected to start later this week, with the president standing on the sidelines, unhappy over versions passed by both houses and threatening to veto individual tax and spending bills that depart from the administration's own budget scenario.

An agreement on a budget will be possible only if the president "gets involved . . . and puts partisanship aside," House Budget Committee Chairman James R. Jones (D-Okla.) warned yesterday in remarks to a conference sponsored by the American Stock Exchange.

O'Neill, in his speech to the same conference, accused the administration of trying to "shift the blame for runaway deficits from the White House to Congress" by, as he put it, "opposing a budget compromise."

Said O'Neill: "I believe that the president is positioning his party for the next election by moving away from bipartisanship," despite earlier cooperation with congressional Democrats on Social Security and jobs legislation.

Saying the economic recovery is threatened by a "fiscal hemorrhage that is currently sinking the federal government in a sea of red ink," O'Neill said Congress should slow the defense buildup and call on "the financially well-off . . . to sacrifice in the effort to reduce the deficit."

He endorsed a 5 percent increase in defense spending after inflation, which is halfway between the Senate's proposed 6 percent increase and a 4 percent increase approved earlier by the House. Reagan had proposed 10 percent.

As for the tax cap, O'Neill predicted that the administration would attack it as a general tax increase, and he was not disappointed.

"We don't see that as anything new from the Democrats," White House deputy press secretary Larry Speakes said only a few hours after O'Neill's speech. "They always want to raise taxes."

Dole also contended that middle-income as well as high-income Americans, including a single taxpayer earning no more than $31,000 and filing a non-itemized return, would be adversely affected by the cap.

O'Neill, on the other hand, said the proposal was only "an effort to make sure that average working families are not the only people carrying the burden of Reaganomics," and added in remarks to reporters:

"It is time that the burden of Reaganomics is shared by those in the upper income groups. For two years, this group has benefited mightily from the Reagan tax program. It has been a program of the rich, by the rich and for the rich. It is time that the rich started to accept their fair share of the burden."

House Democrats are expected to caucus today on the tax issue. They are to be asked later in the week to fill out questionnaires on whether they favor repeal or delay of the tax cut or a cap of $500 or $700, or perhaps other modifications.

The House is expected to act on the caucus' recommendations by June 20, and O'Neill has predicted confidently that, with the heavy Democratic majority in the House, the caucus' proposal will prevail.

In the Senate, Dole is understood to favor voting on the issue as an amendment to a bill to repeal tax withholding on dividends and interest, which is scheduled to come to the Senate floor next week. However, the House would not have acted by then. A final strategy for handling the issue on the Senate floor has not been determined, leadership aides said.

Meanwhile, Rep. Jack Kemp (R-N.Y.), a leading advocate of Reagan's tax cut program, told the stock exchange conference that the top income tax rate should be reduced from the current 50 percent to 15 or 20 percent. Kemp said the change should be made during a second Reagan term. It should be accompanied by similar reductions in tax rates for lower-income taxpayers.