The upcoming Environmental Protection Agency budget will be down 20 percent from this year's request and 29 percent from 1981 figures, the National Wildlife Federation revealed yesterday. The group, the nation's largest environmental organization, said it means "wrongful death by strangulation" for the EPA.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) immediately called the proposed $961 million EPA budget a "radical demolition program" that President Reagan must acknowledge as his own. O'Neill and several other Democrats promised at a news conference that their party will "fight it every step of the way," making it a major campaign issue this year if necessary.

Nineteen House Republicans joined to commend the federation and the Democrats "for bringing the plight of EPA to national attention."

Without confirming the budget figure, EPA spokesman Byron Nelson insisted that the administration "is unflaggingly committed to the protection of the American environment, and we have no intention of slashing at that protection." He called the federation's attack unbecoming, and promised that the EPA's budget "will separate the environmental wheat from the chaff."

Federation President Dr. Jay D. Hair offered a 46-page analysis of the EPA's budget and personnel needs. The analysis, compiled over the last three months by former EPA officials and outside analysts, makes a case for an EPA budget of $2.16 billion.

"The administration could save that amount of money by canceling just one economically and environmentally unsound public works project, the infamous Tennessee-Tombigbee Waterway," he said.

Corrected for inflation, the EPA's budget is down 39 percent from 1981 figures, and means the administration "is moving to cut EPA in half at a time when its workload is doubling," Hair said. The budget provides for 8,645 workers, down 2,762, or 24 percent, from the number of people employed in 1981, he said.

But the EPA is just beginning major programs attacking toxic waste dump cleanup and hazardous chemical control, efforts Hair said will nearly double the workload. He rejected the EPA's position that elimination of bureaucratic waste means that more can be done with less money.

He noted that the book "Fat City," by Donald Lambro, cited by Reagan as the truth about Washington bureaucrats, rated the EPA among the top three best managed federal agencies.

Rep. Morris K. Udall (D-Ariz.), who chairs a new Democratic Party task force on the environment, said the EPA's condition will be "a major campaign issue. It's gonna' hurt the Republicans and hurt them bad, and they'll deserve what they get," he said. "EPA is being mugged in broad daylight . . . . No longer is there any tenable case that these are zealous bureaucrats doing this on their own."

Rep. Albert V. Gore Jr. (D-Tenn.) said the administration "has gone out on an extreme right-wing limb" in proposing this budget. He predicted that public sentiment would grow to support higher EPA spending. "It is time for Congress to intervene. We will," he said.

Rep. Thomas J. Downey (D-N.Y.) released a report by his state Department of Environmental Conservation on the impact of the cuts on New York City and Long Island. Of 32 states with environmental agencies, he said, New York is the only one with resources for such a study. "The slack is not, cannot, will not be picked up by local government," he said.

The federation's alternate budget, billed as "the first fully independent, detailed, reliable statement of EPA's real program needs," would triple the EPA's budget in hazardous waste, toxic chemical and pesticide control and double it to preserve research, clean water and clean air. Management funding would be increased by half. Total personnel would be doubled to 16,357.

The study, distributed to the White House and all members of Congress yesterday, included charts comparing the EPA's "work per worker" with other agencies, finding the agency more efficient.

Hair said it is "a political falsehood" that EPA Administrator Anne M. Gorsuch has been fighting against even more budget cuts. Asked whether he thinks the Reagan administration cares about the environment, Hair had a one-word answer: "No."