Tax relief won't come this year and the whole budget process could collapse if House Democrats continue what Republicans consider a plodding pace on administration proposals, the Senate Finance and Budget committee chairmen warned yesterday.

But House Ways and Means Chairman Dan Rostenkowski (D-Ill.) vowed House Democrats would take their time considering tax and budget legislation, aiming to put a tax bill on President Reagan's deak by the end of September. That is nearly two months past Reagan's Aug. 1 deadline and too late for a 1981 cut, according to Finance Chairman Robert J. Dole (R-Kan.).

Rostenkowski, speaking on Cable News Network's "Newsmaker Sunday," said, "I should imagine that everybody in the administration . . . would like to see things done a little faster.

"Heck, I'm sure that the president didn't realize the process of legislation. We're moving at this point in time with respect to . . . the largest tax cut in the history of this nation. We're moving at a faster pace than I had imagined that we could move."

Dole, on "Issues and Answers" (ABC, WJLA, said if a tax bill isn't agreed upon by Oct. 1 it would be too late to implement a tax cut this year. Dole noted Congress will recess five weeks beginning in August and one week for Independence Day, starting Friday.

"So if they [the House] can stall around until after the August recess to take up the tax bill, the individuals aren't going to get any tax relief in 1981," Dole said.

The president has proposed a 25 percent tax reduction plan over three years. Reagan had hoped to have his tax program in place by Oct. 1 and had set an Aug. 1 deadline for congressional action.

Dole said he hopes to put pressure on the House by developing a tax bill and sending it to the Senate floor, even if the House hasn't acted.

"We want to get it on the floor, maybe even take action on the floor so that when the House does move, we're ready to go," Dole said.

Meanwhile, Sen. Pete V. Domenici (R-N.M.), on "Face the Nation" (CBS, WDVM), criticized House Democrats for not sticking close to the administration's goals in the budget resolution they adopted earlier this year. The Budget Committee chairman warned that slowness on spending cuts could also jeopardize the Reagan tax plan's future.

Rather than follow administration goals, House committees have been redesigning the president's program to his dissatisfaction, prompting Reagan to propose on Friday $20 billion more in spending cuts over the next three years.

The administration has said that although the House has made cuts comparable to those sought by the president in dollar terms, they don't cover the same programs and thus will have a weaker effect on future budgets.

Domenici said the House and Senate differ on eight or 10 major issues, and warned that when the two bodies go to conference on the budget, that effort could fail because they're too far apart.

"There is a real probability that we would not get that bill of conference," Domenici said. "If we don't get it out of conference, that means the cuts are not made, that means the tax package is in jeopardy and . . . we have delayed the president's economic recovery plan beyond this year." .

Domenici added that if the president's budget proposals fail, the country could face a $100 million budget deficit by 1983.

Dole said he thinks Congress may "lose its nerve" on the budget cuts. Trimming the budget now "is going to be very tough," Dole said.

"It's hard to take the 'me' out of economy."

Reagan's plan introduced Friday would in some cases alter the way the established committees cut programs. Domenici suggested that perhaps eliminating Congress' usual deliberative procedures is acceptable.

"If we leave it up to the basic traditional approach, take plenty of time, let every committee which has invented most of these laws and are strong boosters of them . . . if we want each one of them to take their natural time, this president's term of office will be over with before we effect the cuts."