The Environmental Protection Agency is fast running out of money to clean up toxic-waste dumps and will begin to shut down the Superfund program in two weeks unless additional funds are made available, EPA Administrator Lee M. Thomas said yesterday.

The agency has been operating a pared-down Superfund program since September, when it became clear that Congress would not renew the program before the special taxes that finance it expired Oct. 1.

Congress adjourned last year without completing work on Superfund, and congressional aides said yesterday that prospects for immediate action are not good.

In an effort to stretch the program's remaining funds, EPA officials have postponed engineering studies at dozens of toxic-waste sites and slowed the cleanup pace at others. The next step, Thomas said yesterday, is to halt cleanup work altogether and prepare to furlough more than 1,500 EPA employes.

"We've got major problems," Thomas said. "We're at the point where were going past a slowdown and into a shutdown."

The House and Senate passed bills last year to expand Superfund and renew it for five years, but efforts to reconcile their versions have been blocked by an acrimonious battle over the size of the fund and how to raise the money.

The $7.5 billion Senate version includes a broad-based manufacturers' tax, while the $10.3 billion House version would sharply increase taxes on the petrochemical industry. Lobbying has been intense on both sides, and the White House has threatened to veto both financing schemes.

In his State of the Union address two years ago, President Reagan said he supported continuing Superfund "for as long as is necessary to get the job done." The administration fought efforts to renew the law in 1984, however, saying it was too soon to think about altering Superfund.

The administration also has opposed efforts to provide the EPA with stopgap funding until tax issues could be resolved. In a reversal of that position, Thomas said yesterday that short-term funding would be necessary if a bill is not passed by April 1.

"I'm saying to Congress that . . . you've got to help me out," he said.

Under a "shutdown" schedule released yesterday, the EPA will send advance notices of contract terminations and begin planning furloughs in mid-February.

Superfund director J. Winston Porter said that intends to use $100 million of the program's remaining $140 million to keep employes on through September but that the agency had to prepare well in advance for major dismissals.

By April, funds for emergency toxic-waste removals would be down to $1 million a month, about one-fifth of current levels, and money for active cleanups would begin running out. By July, all cleanups would cease, and the agency would start dismissing legal actions against toxic dumpers.