The fight to change U.S. tort law to ease the current threat of liability lawsuits is shifting to the states. Members of the 50 state legislatures are going to be the main focus as business forms new alliances with physicians, social workers, board of education members and even local United Way organizations, all of whom can be targeted for damages when a victim is injured in a serious accident.

The issue is going to be a hot one on the congressional agenda this year, with Sen. Jack Danforth's (R-Mo.) Senate Commerce Committee opening a series of hearings on the subject Feb. 19. Rep. James J. Florio (D-N.J.), who heads the House subcommittee that handles insurance matters, says that complaints from constituents about how tough it is to get liability insurance -- and how much it costs when it is available -- dwarf every other subject.

But businesses and consumerists, liberals and conservatives, and the Senate and the House, are so far apart on what kind of legislation Congress should pass that it is unlikely that any bill can emerge this year. Even the lobbyists anxious for a new federal law admit that. Said Thomas A. O'Day of the Alliance of American Insurers, "Will a bill pass in '86? The odds are against it."

That's why those seeking reform are concentrating their attention on the states. Even the Cabinet working group headed by Assistant Attorney General Richard K. Williard that is hammering out a Reagan administration position on the problem has decided that position should be centered on the states' taking the lead.

In a couple of weeks, the panel will recommend to tha Cabinet that, while there is some room for Congress to act, the most important thing Washington can do is draft a model state tort-reform statute and lobby state lawmaker to adopt it.

"I don't believe that we should federalize tort law across the board," Williard said. "Ultimately, federalizing our problems is not the best solution." The model statute that the Reaganites will come up with is likely to include a cap on the amount of damages that can be collected for pain and suffering and similar damages that are not measured in out-of-pocket losses. Other possibilities: curbing punitive damages, apportioning each defendant's liability to its degree of guilt for the accident, and limiting the fees that a lawyer can collect in an individual case.

Last month, two new business-lobbying groups were formed to try to change liability laws so it will be harder for plaintiffs to win suits, and both are putting their main emphasis on working with state legislatures:

*The American Consulting Engineers Council brought together such diverse organizations as the National Paint & Coatings Association, the American Trucking Association and the American Association of Community & Junior Colleges into the American Tort Reform Association.

"We intend to carry this effort to 50 state capitals this year," said ATRA Chairman James K. Coyne. "Tort reform will not come only by the efforts inside Washington's Beltway. It will be the number one issue in at least 40 state legislatures this year."

*The U.S. Chamber of Commerce created a National Clearinghouse on the Liability Crisis and kicked it off with simultaneous meetings in New York, Atlanta, Chicago, Denver, Dallas and Los Angeles. The purpose is to encourage business executives to form statewide coalitions in which they can team up with physicians, social workers, city and country elected officials and others threatened by liability suits to present a unified pitch to state legislators.

The chamber will publish a free newsletter to keep each state group informed of strategies and successes of the other state groups. Harvey Alter, head of the resources policy department of the chamber, insisted that this is one of the rare times when a grass-roots movement develops not to oppose litigation, but to initiate it.

Lobbying state legislatures is no easy task, at least partially because plaintiffs' lawyers -- the most solid opposition to tinkering with the current tort system -- so often have a hammerlock on the legislature judiciary committees.

And, in fact, local special interest groups have had far more success in toughening tort litigation in state capitals than they have managed in Washington. In many states, doctors have won new protections against malpractice lawsuits.

Last year, for instance, Illinois barred punitive damages in suits against physicians, required that an independent panel certify a case as meritorious before it can get to trial, and changed the law so that when a doctor wins a case he or she feels was brought maliciously, the doctor can turn around and ask for court sanctions against the plaintiff. Just recently, the Colorado Supreme Court upheld a state law that gives resort owners special protections against suits stemming from skiing accidents. Wisconsin is one of the states that had decided not to hold a bar owner liable for injuries caused by a drunken patron.

Reforms that cut across the board -- that make it harder to bring any sort of liability suit or that make it harder to win big damages in such litigation -- are a lot more rare. But they have occurred.

Arizona and North Dakota, for instance, last year made it mandatory for plaintiffs losing suits that are deemed to be frivolous to pay the defendant's legal bills. And Montana decreed that a company should never be charged punitive damages of more than 1 percent of its net worth. It is those kinds of reforms that the new state-centered coalitions are hoping for this year.