The dramatic drop in interest rates now underway could cut deeply into the federal budget deficit, adding a politically painless dividend to the budget actions approved by Congress last week.

If interest rates stay where they are now, the government could save more than $10 billion in interest on the national debt during the next fiscal year, which begins Oct. 1, say economists at the Office of Management and Budget.

Because of the sharp decline in interest rates in the past eight weeks, the rate the government has to pay to borrow money via Treasury bills is now about 3 percentage points lower than projected in the 1983 budget. The government had figured it would have to pay an average of 10.7 percent interest on 91-day Treasury bills, but now the T-bill rate is down to 7.7 percent.

OMB economists said any estimates of the impact of lower rates on Treasury debt are rough ones. But they estimate that every one percentage point decline in T-bill rates saves the government between $3.2 billion and $4.1 billion a year in interest.

If rates hold near that level for the next 14 months, interest costs would be between $10 billion and $12 billion less than assumed.

But Robert Weintraub, of the Congressional Joint Economic Committee, said that because many purchasers of T-bills pay taxes on the interest they receive, government revenues decline somewhat when the interest paid by the Treasury on U.S. debt falls. The lost revenue because of lower payments to taxpayers has to be deducted from the interest the government saves, so the total effect on the budget deficit would be somewhat smaller than the reduction in Treasury outlays.

Interest rates on longer term government bonds have not come down as much at Treasury bill rates, however. As a result, the sharp decline in bill rates may not result in quite as big a savings in interest outlays as would occur if long-term rates came down as fast as short term rates have.