The Congressional Budget Office projects that the federal deficit will rise to $157 billion in the current fiscal year and to $176 billion in fiscal 1989, well above the ceilings set by law, according to congressional sources.

The projections, which the CBO will present to the Senate Budget Committee today, provide evidence suggesting that despite the recent budget agreement between the White House and Congress, the deficit is likely to widen.

The budget accord was supposed to shrink the deficit from the fiscal 1987 level of $148 billion to the target levels set by the Gramm-Rudman-Hollings law. The law sets deficit limits of $144 billion in fiscal 1988 and $136 billion in fiscal 1989.

But the economic forecast on which the accord was based was more optimistic than many economists believe credible for the next two years. A forecast of rapid economic growth tends to shrink the projected deficit because of higher tax receipts, while a forecast of slower growth tends to cause projected revenue to fall -- and the deficit to widen.

As previously reported, an internal White House budget analysis shows that the deficit would grow to $158 billion in fiscal 1988 and $167 billion in fiscal 1989 if the economy performs as most private forecasters expect.

Nevertheless, President Reagan's own budget is expected to project deficits that meet the requirements of the budget law because the administration is more bullish about the economy -- especially in 1989 -- than are private economists.

The administration's deficit estimates may allow Congress to get through the election year without another nasty budget fight. Under the law, the administration's figures are used in determining whether the budget law's requirements have been met.

The CBO expects growth that is considerably slower than the administration's forecast, as well as interest rates that are higher. High interest rates cause the deficit to widen by increasing the cost of debt service.

The CBO forecasts economic growth of 1.8 percent for 1988 and 2.6 percent in 1989, according to the congressional sources. It forecasts that interest rates on 10-year Treasury bonds will average 9.3 percent in 1988 and 9.5 percent in 1989.