The chairman of the House Democratic Caucus says there will be no attempt to freeze Social Security cost-of-living increases unless President Reagan changes his rhetoric, but warned that Democrats may find it difficult to put together a significant deficit-reduction package if they automatically rule out an examination of Social Security.

"I think the overwhelming sentiment is not to touch Social Security and I would predict we would not do anything on Social Security," Rep. Richard A. Gephardt (D-Mo.) said in an interview in his office. "But . . . this is a tough set of budget numbers. When you put anything off bounds, saying you would not even think about it, you can often find yourself in a position where the other alternatives are as difficult, if not more difficult."

In Reagan's news conference Wednesday night, he said that, despite his campaign promise not to cut Social Security benefits, he might accept a freeze on the Social Security cost-of-living adjustment (COLA) if "faced with an overwhelming bipartisan majority in both houses" in support of a freeze.

"It's part of the frustration of dealing with Reagan," Gephardt said of the president's comments. "It drives people up the wall."

He said any chance of House Democrats considering changes in Social Security "requires a change in Reagan's rhetoric. If Reagan continues to say, 'If Congress forces me to look at this I'd consider it,' it's not going to happen."

Gephardt said he thought a tax increase could be approved by House Democrats without Reagan initiating it, but said the White House would have to endorse it and support it. Reagan said Wednesday that he continues to oppose any tax increase.

Senate Republicans, led by Majority Leader Robert J. Dole (R-Kan.), have been considering a freeze on cost-of-living increases for Social Security recipients as part of an overall budget freeze. That step alone would save about $6 billion in the first year.

House Majority Leader James C. Wright Jr. (D-Tex.) said Thursday that the House "will not be party to any [effort] such as that." He said Democrats would help Reagan "keep his promise."

House Minority Leader Robert H. Michel (R-Ill.) agreed, saying House Republicans fear political reprisal from Democrats, as happened in 1982, if the program is cut.

Gephardt, one of the young leaders of the House Democrats, said there are ways to deal with the issue other than by freezing payments. He cited changing the formula for COLA payments or consideration of a means test, under which wealthier recipients of Social Security might see their payments reduced.

"I am not personally desirous of doing Social Security," Gephardt said. "It's on its own track" and is not adding to the federal deficit, he said.

But he said there are other problems of equity in ruling it off the table in early examinations of a budget resolution.

"If we go to military pensions or civil service pensions and say we're going to slow down the COLA or put a means test on and [we] don't do that with other pension programs, then the people [we're] affecting have a wonderful and effective argument saying you're not being even-handed."

Gephardt continued, "If you put off base all pension programs, then the cuts you come in with or the taxes you've got to come in with [to reduce deficits significantly] become that much more difficult."

He predicted that when House Democrats begin their deliberations on the budget, "they will continue to not want to do Social Security . . . , but what they're left with may be so difficult, they may want to go back and say what possibly could be done. Even then, if [Reagan] continues to play his rhetoric the way he's done, I think it's not going to be doable."