House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said yesterday that House Democrats are giving overwhelming support to his proposal to limit the July 1 personal income tax cut to $700 per return.

O'Neill said he had received more than 200 responses to his poll of the members as of late yesterday and that his plan was "running away with" the vote. Staff aides said the Democrats, with a 99-seat majority, clearly have enough votes to pass and send a tax-cut curtailment to the Senate.

O'Neill said he would not make full details available until he had discussed the results with Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.), who is out of town.

Rostenkowski has not been eager to assume the political burden of reporting out a revenue bill, but he has told reporters that he reluctantly will go along with the House Democratic leadership.

It is uncertain whether a tax-cut limit can pass the Republican-controlled Senate. Even if it does, it appears unlikely that there are enough votes to override a veto promised by President Reagan.

Sen. Dale Bumpers (D-Ark.), a leader of the campaign for the tax-cut ceiling in the Senate, said it was "hard to say" how many Republicans would support it. Asked what would happen if opponents mustered 34 votes, enough to sustain a veto, he said, "then we will not prevail."

A family of four would be affected by a $700 ceiling or cap on the tax cut only if its adjusted gross annual income exceeded about $50,000. Approximately 89 percent of all taxpayers are expected to receive reductions of less than $700, the Democrats contend, which means that only those in upper-income brackets would be affected.

It has been estimated that a $700 cap would increase federal revenue by about $6 billion in fiscal 1984, scarcely denting a deficit expected to be at least $174 billion. But the Democrats are gambling that it will pay off politically, showing them to be the party of fairness and responsibility.

"This at least would show some resolve on the part of Congress" to do something about the deficit, Bumpers said. "At some point we all have to wake up to the fact that no cosmic event is going to save us."

Republicans who oppose the cap are portraying the Democrats as the party of higher taxes and unrestrained spending, because they have not offered budget-cutting proposals along with the limit on the tax cut.