The government may begin bouncing hundreds of thousands of checks today unless Congress reaches agreement this morning to increase the amount the government can borrow to pay its bills.

If the money runs out before Congress moves to increase the debt ceiling, it would be the first time that federal government checks would have to be returned for insufficient funds.

Senate leaders early this morning hammered out a deal that would pave the way for approval of a stopgap extension of the Treasury's borrowing authority. The breakthough came after nearly 15 hours of acrimonious debate in which Republicans and Democrats remained deadlocked over terms of a short-term extension of the debt ceiling. A vote on the deal is expected today.

Treasury officials said yesterday that they would continue to issue checks despite their estimate that the government's cash position would become negative sometime today.

If the stopgap plan is passed today, Treasury Department officials said they could avert the first U.S. default by selling $5 billion of Treasury bills at an auction hastily planned for 12:30 p.m. today. However, they would need the authority of Congress to do so by this morning, officials said.

"In anticipation of action that would allow us to proceed with this financing, we and the Federal Reserve should be able to manage payments so as to avoid a default," said Deputy Treasury Secretary Richard G. Darman in a letter to the Senate leadership yesterday.

The Treasury announced its intentions to sell the short-term securities yesterday. The Darman letter also said that the government would have a negative cash balance today. Treasury officials said that they would decide this morning what other actions can be taken to avoid default if Congress doesn't act in time for the auction to be held.

According to the Treasury's financial management service, the Treasury issues 600 million checks annually, which would average about 2.4 million every business day.

"It's business as usual until we are told otherwise," said a spokesman for the department that writes checks for Social Security, veterans benefits, civil service and other government retirees, interest on government notes and bonds, payments to firms that do business with the government, and federal salaries.

The Defense Department, the Tennessee Valley Authority, the U.S. Postal Service and several other agencies issue 150,000 additional checks annually, the spokesman said.

If the government accounts are overdrawn, the Federal Reserve -- the Treasury's bank -- will return the check to the bank where it was cashed in the same way that a commercial bank would return a private check to the customer that tried to deposit a bad check, according to a spokesman for the Fed.

Treasury Department officials said that since the Congress is expected at some time to pass a debt ceiling bill, the government check eventually would be honored.

The Reagan administration has sought to increase the amount of debt it can issue from $1.824 trillion to $2.078 trillion.

The debt ceiling legislation has been held up by debate over a measure that would force the government to balance the budget by 1991.

Earlier yesterday, Senate Majority Leader Robert J. Dole (R-Kan.) said that he hoped to take action on a short-term extension of the debt ceiling today. That bill would extend until Oct. 17 the government's authority to issue debt and would give the House of Representatives time to complete action on the measure and send it to the president to be signed today.

Darman said yesterday that the government's choices were "an unprecedented default by the United States" or the "unprecedented and questionable use of Federal Financing Bank authority" to borrow money to pay the government's debts.

Congress established the FFB in 1973 to coordinate sales of government securities issued from independent federal agencies. It also has the authority to sell up to $15 billion worth of securities to the public, a Treasury official said.

What the Treasury could do is have the FFB sell securities to the public in return for cash to increase its cash balances. However, in letters to Congress earlier this month, Treasury Secretary James A. Baker III said that that practice was unprecedented and possibly could violate the intent of Congress in establishing the FFB.

Additionally, debt issued by the FFB might have to pay a higher interest rate than regular Treasury securities, generally considered the least risky debt instruments around, officials said. Consequently, the FFB securities would cost the government more money.