The federal government, which has vowed to crack down on overdue taxes, student loans and other late payments, has problems paying billions of dollars of its own bills on time.

The government pays about 30 percent of its bills after 30 days, the General Accounting Office estimates, with the average late bill paid 74 days after billing. The overdue bills represent about 18 percent of the dollar value of the federal government's purchases, the GAO said.

Assuming $100 billion worth of procurements each year, the GAO estimated that the government paid about $18 billion worth of bills after 30 days. With a 12 percent interest rate, it said, that represents a cost to contractors of between $150 million and $375 million each year in interest that the money could have been earning or in what they might have had to borrow.

The GAO noted, however, that in paying 70 percent of its bills on time, the government has a "reasonably good" record.

But that's not good enough for some small businessmen, who have complained to Congress about the problem. In December the Senate passed a bill that would require agencies to pay interest on late bills--at a rate set by the treasury secretary with the going rate for five-year treasury bills as a guideline. Similar legislation is pending before the House.

The Reagan administration opposes the legislation, however, saying it would be too costly.

Kenton Pattie, a Virginia businessman who has organized a group called the Slow Pay Coalition to fight for prompt payment of the bills, said, "The goal of the penalty interest is to put the buying agencies on equal footing with the small businesses. If a small business is late in paying federal taxes, it pays an interest penalty."

The American Consulting Engineers Council, for instance, found that on average last year, the government paid its members 2 1/2 months after billing, forcing the private engineering firms to borrow an average of $225,000 each.

Some companies, like Behrens Inc., a Texas pharmaceutical firm, have "made a corporate decision to wean ourselves from federal accounts," said Vice President Bill Clifton. "We can no longer afford to service them. You can only take this mistreatment for so long. You don't feel like subsidizing the federal government when you're already paying taxes."

Behrens' largest federal customers were Veterans Administration hospitals and the Air Force. He said the firm has completely cut off the VA because of consistently late payments and still carries some Air Force accounts, "although very few because we're always writing letters to the base commanders to get paid."

Ronald D. Henry, president of a Washington audio-visual equipment store called AVCOM, said his firm also has decided not to take on too much government business, "simply because small business can't afford to."

"The government just doesn't pay," he said.

Contractors said some agencies are better than others in making payments on time; a number singled out the Internal Revenue Service as being notoriously bad, while the FBI and the CIA were thought to be extremely efficient.

In recent testimony before a House committee, Edwin L. Harper, deputy director of the Office of Management and Budget, stressed that more than 80 percent of the total value of the federal government's bills is paid early or on time, but he acknowledged that there is a problem with overdue payments.

However, he said that the administration opposes the pending legislation and contended that OMB is making progress on its own.

Harper labeled the House bill "costly" and estimated it would cost $37 million a year to administer the program, in addition to the interest payments the government would have to make.

The legislation would forbid additional appropriations for the interest payments, forcing agencies to pay the penalty out of their existing budgets. Sen. John C. Danforth (R-Mo.), who sponsored the bill in the Senate, argued that because of that provision, the bill would not cost the taxpayers anything. But Harper called that claim "Alice-in-Wonderland accounting."

Harper cautioned that the measure did not allow for improper or incorrect billings by contractors, disputed billings and staff limitations. The bill "would increase errors in payments, result in more overpayments and open the door to more fraud, abuse and waste of taxpayers' money," he said. "It would do this by putting inordinate pressure on payment centers to pay bills, regardless of whether proper documentation was available."

He also contended that much of the overpayment problem was the fault of contractors. But the GAO said its figures were adjusted to account for errors by contractors.

Harper noted that last September OMB had urged all federal agencies to include specific payment terms in each contract and the name of a person who would be responsible for the contract's payment. He said preliminary results indicate "that real progress is being made."

A recent follow-up, he said, found that of 44 departments and agencies reporting, 30 had late payment problems with less than 2 percent of their invoices and 23 with less than 1 percent.

But Washington businessman Henry is skeptical that anything short of interest payments will improve the system. "With interest payments, it would become very political," he said. "It would be difficult to explain to the taxpayers why $1 billion a year was spent on interest payments on bills that were not paid on time simply because the system is so screwed up."