Treasury Secretary G. William Miller asked Congress yesterday to increase the ceiling on the national debt by $56 billion before the end of the month so that the government can keep paying its bills.

Miller told the Senate Finance Committee that the government will have to borrow $200 million during the fiscal year beginning Oct. 1 to pay of maturing securities and $60 billion to finance new debt. The amounts are about the same as for this year, he said.

Earlier in the day, Miller appealed to the House Ways & Means Committee for prompt action because the present temporary debt limit of $830 billion reverts to the "permanent" limit of only $400 billion on Oct. 1.

In the last two years, Congress has considered increasing the debt limit four times, Miller said. "On three occasions, action was not taken before the expiration debt, and the Treasury was unable to borrow until the Congress acted two or three days later," he said.

The dalays meant the Treasury incurred "significant cost" and had to take "extra ordinary measures . . . to prevent the government from going into default," Miller said.

"The Treasury was required to suspend the sale of United States savings bonds, and people who depend upon Social Security checks and other government payments suddenly realized that the Treasury simply cannot pay the government's bills unless it is authorized to borrow the funds needed to finance the spending programs previously enacted by Congress," he continued.

Members of Congress frequently have opposed increases in the debt limit, even though they know one must be passed, to be on record as favoring economy in government.

Saying that the present process "may actually divert public attention from the real issue -- control over the federal budget" -- Miller proposed that changes in the debt limit be incorporated in Congress' annual consideration of spending and taxing targets in its budget resolutions.

And the Treasury secretary also asked that the $40 billion limit on the amount of outstanding long-term securities be raised to $55 billion so that the Treasury could continue to lengthen the average maturity of the debt.

W. Bowman Cutter, executive associate director of the Office of Management and Budget, told the Ways and Means Committee that the latest estimate of the budget deficit for fiscal 1979, which ends this month, is now $30.3 billion, up $600 million since the last estimate in July.

The new figure for fiscal 1980 is $29.4 billion, up $700 million from the July estimate.

Cutter said the debt limit must be increased by nearly twice the amount of the unified budget deficit because the limit also applies to debt securities that the Treasury issues to trust funds such as Social Security whose surpluses reduce the reported deficit. In addition, the Treasury borrows on behalf of some so-called off-budget agencies, federal entities such as the Rural Telephone Bank.

In fiscal 1980, the trust funds will have combined surpluses of $17.9 billion, and the off-budget agencies will have a deficit of $11.6 billion, Cutter said.

During questioning by Ways and Means members, Miller reiterated his opposition to a tax cut at this time. "At this stage . . . a $30 billion tax cut would not only increase our deficit, but it would also be inflationary," Miller declared.

"I do not believe at the present time it would be wise to consider such a cut," he added.

Also yesterday, Miller told a neeting of the National Governors Association that the "only way to get interest rates down" is to "get inflation down." He said that the Federal Reserve Board's policy of high interest rates has been "inevitable" in the face of inflation.