President Carter is facing another thorny -- and politically embarrassing -- decision on his controversial plan to cut spending for federally-financed public service jobs under the Comprehensive Employment and Training Act.

Last November, White House planners stirred a storm of protest from blacks and other groups by proposing to slash spending for these programs by $2.6 billion -- a move that would have cut 440,000 jobs from the 625,000 on the books.

In December, bowing to liberals' pressure, the president "restored" $1 billion of that money. Job levels for fiscal 1980 now were to average 540,000, declining to 467,000 by September 1980. Liberals still were upset over the cuts.

Administration officials have since discovered that attrition and local shutdowns already have pared CETA jobs to 517,000 -- well below the 625,000-mark planners thought existed when they made the cuts.

Carter's dilemma now is whether to expand the CETA program back to the 625,000-job level between now and this Oct. 1, the start of fiscal 1980 -- particularly the portion of the overall program designed to help the hard-core unemployed.

Administration strategists fret Carter may come under even more criticism from blacks and other groups if that portion of the program is not kept to target levels. The president already has taken heat over general cutbacks.

At the same time, the White House already is in trouble with the program's critics, such as Sen. Lawton Chiles (D-Fla.), who held back on making deep cuts last August after Carter argued it would wreck the program.

Meanwhile, officials say that new figures have left about $1 billion in unused money "sloshing around" in the fiscal 1979 budget that could affect the fiscal 1980 spending plan as well.

Top administration officials have been meeting privately over the past few days to try to work out a plan for dealing with the situation.So far, however, the White House has not agreed on a strategy.

The newly discovered drop in the actual number of job slots across the country stems in large part from cutbacks by state and local governments in the face of mounting congressional displeasure with the CETA program.

Officials say the congressional cutbacks enacted last fall came within a few weeks of the time that most states and localities had to renew their contracts to operate CETA jobs programs. Most saw the trend and retrenched.

Officials say the drop first appeared to policymakers in a report last Sept. 30, which showed only 596,000 slots actually filled, rather than the 625,000 on the books. But planners regarded this as only an aberration.

A later report showed only 517,000 job slots actually filled as of last December, but the figures reached policymakers only in mid-January, after the budget already had gone to press.

Ironically, the 517,000-job level is approximately that sought by critics during last autumn's congressional debate. Chiles, for one, had wanted to cut CETA money sharply, but settled for a 100,000-job cut at Carter's insistence.

In late fall, Congress passed a continuing resolution giving the program essentially the same money in fiscal 1979 as it had the previous year, but ordering Carter to pare the total to 625,000 jobs, through attrition by next September.