Chiding President Reagan as a late comer to tough action on America's burgeoning trade deficit, House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) predicted yesterday that the new White House trade initiative is unlikely to stop House consideration of protectionist bills.

He told a Capitol Hill press conference that the president's "strategy of slowing the push for tough trade policy isn't working" and promised "a crippling fight with Congress" if the new Reagan program fails to bring "retribution against countries who keep out, or unfairly drive up the price, of U.S. products."

White House aides said President Reagan will probably unveil his new trade policy in a major speech, perhaps as early as next week.

The new program, which received presidential approval Wednesday after congressional Republicans described a brush fire of bipartisan support for tough trade bills, is likely to include legislation toughening existing laws against unfair trade practices, a $300 million war chest to meet subsidized export financing by other countries and new laws to combat piracy of American copyrighted material and patents.

Rostenkowski said the first congressional action on trade will be Ways and Means Committee approval by the end of the month of a bill to drastically cut textile imports. Even though he opposes the textile bill, Rostenkowski indicated he is moving it forward because he can't stand in the way of the vast majority of House members from both parties who support it.

Rostenkowski's decision to allow committee approval of the textile measure sets the stage for a major confrontation between an increasingly frustrated Congress and the White House, which has threatened to veto any protectionist measures that are passed. With the trade deficit expected to soar as high as $150 billion this year, Congress has more than 300 bills trade bill in the hopper.

On the Senate side of the Capitol, Sen. John C. Danforth (R-Mo.) said the Reagan administration's refusal to enforce unfair trade laws has forced Congress to take the lead.

"I don't like the idea of Congress managing trade policy. I don't think there is any substitute for a trade policy from the White House," said Danforth, chairman of the Senate Finance Committee's trade subcommittee, at the second day of hearings on the textile bill which has a majority of senators as cosponsors.

But the GOP senator blamed White House inaction on trade problems for shifting the issue to Congress, where protectionist pressures intensified when President Reagan last month overruled an International Trade Commission recommendation and refused to grant import relief to the U.S. shoe industry.

"When people bring [unfair trade cases]they should have some reasonable chance of getting relief," Danforth said. The shoe industry, following Danforth's advice, filed an unfair trade case, but "after years of effort they were told they were suckers," the senator continued.

"The result is what we see here today -- large groups of people waiting outside the hearing room to appeal for special legislation," he said.

Danforth said he is on the edge of supporting the textile bill, which he previously had opposed, and has been trying to join to it legislation establishing quotas on shoe imports.

Rep. Cecil Heftel (D-Hawaii) told the Danforth subcommittee he opposes the textile bill, which would hurt his state, even though he signed on as a cosponsor. He said many congressmen joined as cosponsors "as the only way to express frustration and to let constituents know they are trying to do something about the problem."

"Some of my Democratic collegues hope the president will keep his head in the sand [on trade] long enough to cost Republicans" seats in the 1986 House and Senate elections and in the 1988 presidential race, Heftel said.

Rostenkowski told House aides he regretted that Reagan described his new plan as "a Republican trade policy," and added, "What we need is a national trade policy, not a Democratic or Republican one."