Unless there is a last-minute rescue by the Supreme Court, the nation's bankruptcy courts, which administer more than $100 billion in assets and hundreds of thousands of jobs, may be thrown into legal chaos today.

Congress attempted to address the problem Friday as it scurried toward the election recess. There were frantic negotiations to reach a compromise to clarify the legal authority of the more than 220 bankruptcy judges, but the two sides were too far apart to make a quick resolution possible.

The bankruptcy courts were left in confusion June 28 when the Supreme Court found the current system of non-tenured judges unconstitutional. The Supreme Court stayed its decision until today to give Congress time to act.

The Solicitor General's office filed a motion in the Supreme Court Friday asking for an extension of the stay until Dec. 24 to give Congress more time to act during the lame-duck session scheduled to begin Nov. 29.

It said the time extension is necessary "to avoid the uncertainty, possible economic loss, and waste of judicial resources that would result from a lapse in bankruptcy court jurisdiction."

Dean Gandy, president of the National Conference of Bankruptcy Judges, said in an interview that unless the issue is resolved, "bankruptcy, as a viable option in the solution of debtor and creditor problems, will be pretty well eliminated."

Meanwhile, he said, businesses in bankruptcy reorganizations face a danger of failing completely, and individuals could unnecessarily lose homes and other possessions.

After Congress reformed the bankruptcy code in 1978, judges routinely began to decide all of the issues in bankruptcy cases, whether or not they fall strictly under the narrow bankruptcy code.

But the Supreme Court found that Congress gave the judges too much authority without giving them the full protection of regular federal judges who have life tenure and the guarantee of no salary reduction. It found that bankruptcy judges were dealing in areas under U.S. district court jurisdiction.

The problem, Gandy said, is that many bankruptcy cases involve much more than that narrow area of the law. Real estate law is frequently involved, and in many bankruptcies, particularly business cases, judges must solve disputes about debts, taxes and business transactions that do not come under the bankruptcy law.

With 527,342 bankruptcy cases filed in the year ended June 30, Gandy said sheer volume precludes referring bankruptcy cases to overburdened district courts.

Congress is in conflict on two major areas. One involves the status of the bankruptcy judges. House Judiciary Committee Chairman Peter W. Rodino Jr. (D-N.J.) wants simply to elevate them to full federal judicial status with tenure and a guaranteed salary.

But the Judicial Conference of the United States, the top policy-making body of the federal courts, wants the bankruptcy judges to keep their inferior status and would leave legal questions beyond the bankruptcy statutes to the federal district courts. Critics have accused the Judicial Conference of being overprotective of its turf.

In addition, some Democrats have complained about turning over to the Reagan administration the political plum of 227 judicial appointments, an increase of 44 percent of the current number of federal judges.

The other major dispute involves companion legislation being pushed by the consumer credit industry to force many individuals filing for bankruptcy to pay off all or a portion of their debts through future income.

The legislation has many congressional supporters but faces serious opposition from Rodino, who has vowed to keep it from moving through the House, and in the Senate from Howard M. Metzenbaum (D-Ohio), who said Friday that he will filibuster against any bill containing that provision.

In an effort to resolve the situation, Rep. M. Caldwell Butler (R-Va.) introduced a compromise bill late Friday. It would elevate bankruptcy judges to full, life-tenured federal judicial status in a division within the federal court system and would allow them to serve on other federal cases if their caseloads should diminish.

The bill also contains noncontroversial changes the courts have requested and other amendments the Senate wants. The most controversial portion is a weakened version of repayment provisions sought by the consumer credit industry.

It is not clear whether Rodino and Metzenbaum will agree, but Butler said he is open to compromise.

Jonathan Rose, assistant attorney general in charge of legal policy, said he believes the administration will support the Butler compromise.

He added that the administration will push Congress to resolve the issue in the lame-duck session. "We simply have to have a legislative solution. The Supreme Court can't be expected to wait forever."