Congress last night broke a stalemate that had threatened to delay two more years any federal plan for disposing of the nation's high-level nuclear waste and sent to the president a compromise bill that would establish a permanent geologic repository by the mid-1990s.

The Senate acted first, yesterday afternoon. Then the House on a 256 to 32 vote agreed last night to 17 Senate amendments after Chairman Morris K. Udall (D-Ariz.) of the Interior Committee warned that any further refinements "would kill the bill."

Rep. Edward J. Markey (D-Mass.) objected that the bill would have the federal government pick up the tab for storing and transporting nuclear waste that should be the responsibility of private utilities. Environmentalists also opposed the bill, which sets up a fast-track procedure limiting environmental and judicial review of disposal sites.

In other action as the lame-duck session of Congress moved toward a close, the Senate Finance Committee blessed a House-passed bill embodying the second half of President Reagan's Caribbean Basin initiative, and the House passed and sent to the Senate legislation providing for a newer but much smaller Law Enforcement Assistance Administration.

House approval of the anti-crime bill, which would dispense $170 million in criminal justice grants to state and local governments, came as key congressional leaders met privately to decide whether to go along with the latest Senate version of the nuclear waste package.

The Senate rushed through the bill in 15 minutes after a deal was struck that greatly strengthened a state's ability to object to its selection by the federal government as the initial burial site for the nation's nuclear wastes.

The original version of the bills passed by both houses provided that even if a state opposed selection of a site within its boundaries, that site still would become the permanent repository unless the state could get one house of Congress to support its objection.

Opponents of this provision argued that it would be difficult to persuade the relieved representatives of the other 49 states to come to the protesting state's rescue.

The compromise bill, however, gives a state a far greater ability to veto its selection. It provides that if a state formally objects to the effort to locate the permanent repository within its boundaries, that site would be eliminated unless both houses of Congress vote to override the state veto.

If the House joins the Senate in passing the compromise waste bill, the president is expected to sign it despite the administration's opposition to strengthening a state's ability to block selection.

The administration and the nuclear industry have lobbied hard for enactment of a bill to dispose of spent fuel that has accumulated for 25 years in storage pools next to the nation's 82 operating atomic power stations. Some utilities say they expect to run out of room to store more spent fuel in the next few years.

The compromise legislation calls for the Department of Energy to conduct environmental assessments of five potential sites and recommend three of them to the president for more detailed study by Jan. 1, 1985. The president then would be expected to make a final decision on one site by March 31, 1987.

The process calls for the president to select a second permanent waste disposal site by March 31, 1991.

Once a site has been selected, the Energy Department would have to prepare a full environmental impact statement, and Nuclear Regulatory Commission procedures would apply to the process leading to construction and licensing of the repository.

While the repository is being built, the legislation requires utilities to take measures wherever possible to continue storing their own spent fuel. But as a last resort, the bill requires the federal government to provide "away-from-reactor" storage for a limited amount of spent fuel at an existing government facility.

The bill also requires that the Energy Department propose to Congress by June, 1985, three to five sites for a "monitored, retrievable storage" facility where spent fuel could be stored in anticipation that the government might wish to remove it and later recover plutonium contained in it.

All of these facilities would be paid for by a one mill-per-kilowatt-hour surcharge on power generated by nuclear reactors. While utilities would be required to pay this fee, they could add it to customers' electric bills where public utility commissions permit.

This fee, which the government probably would start collecting in mid-1983, would raise about $400 million in its first year.

While the bill provides for burial of the vast quantities of high-level radioactive waste generated during production of nuclear weapons in the same repository as civilian waste, the president could order that defense wastes be buried at a separate site for security reasons.

Senate passage of the nuclear waste bill came as many supporters were beginning to fear the legislation was doomed to the fate of an effort two years ago, when bills passed by both houses died in conference.

Supporters of the legislation were particularly distressed at the prospect of having to start again in a new Congress, because the bills that culminated in yesterday's compromise were the result of delicate negotiations involving seven House committees and two Senate committees.

The anti-crime bill would establish an office to finance programs aimed at keeping career criminals in jail, helping elderly victims and running "sting" operations and arson probes.

The bill also would create a White House "drug czar," force drug smugglers to forfeit property, increase penalties on repeat offenders who use handguns and make it a federal crime to assault a CIA employe.