The Treasury Department is gearing up for possibly the first default of the U.S. government.

If Congress does not agree before Friday to raise the limit on the amount the government may borrow, the government will find itself with about $9 billion on hand to cover $16 billion in interest on the public debt that is due that day in addition to some payroll and other checks, Treasury officials said.

If the Treasury's coffers become empty, it must notify the Federal Reserve, which would tell banks not to honor government checks, officials said.

Among those whose checks are due out on Friday are active duty military personnel and employes of the Federal Home Loan Bank Board, National Science Foundation, Railroad Retirement Board and the office of the administration of the U.S. courts.

On Monday, payroll checks are to be issued for some employes of the Energy Department, National Aeronautic and Space Administration workers at the Langley Research Center and Internal Revenue Service personnel.

So far, the Treasury has kept going by using funds from the Federal Financing Bank, which is not subject to the debt ceiling, and manipulating Treasury securities held by the Social Security Trust Fund.

But Treasury Secretary James A. Baker III has said he has exhausted his options for juggling the government's books and will not begin selling gold reserves unless President Reagan asks him to do so. But the president, in fact, has indicated that he will not allow the gold to be sold.

If the government fails to pay the interest owed to lenders, it could create chaos in financial markets, force the government to pay higher interest rates and open the government to possible damage suits, financial analysts have said.

But Treasury Department officials have a more personal reason to be worried about the impasse. They, too, are paid on Monday. And without new borrowing authority, their own paychecks will bounce, officials said.

PERSONNEL FILE . . . Charles Sethness, former associate dean for external relations at Harvard Business School, has been confirmed by the Senate to be assistant secetary for domestic finance to replace Tom Healey, who left to join the private sector.

George Gould is awaiting confirmation by the Senate to be undersecretary of the Treasury. His appointment was approved by the Senate Finance Committee last August and by the Senate Banking Committee last week. The banking committee wanted to have a hand in the process after conflicts arose over Gould's confirmation.