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This morning a report from payroll giant Automatic Data Processing and Macroeconomic Advisers posted a smaller-than-expected decline in private-sector jobs, but it may not say much about the official government figure released on Friday.

The first caveat is that ADP only looks at private-sector jobs, but the Bureau of Labor Statistics employment report’s includes government jobs as well. Government jobs have only had a minor impact in recent months, adding just a net 2,000 jobs in the first quarter. Ian Pollick of TD Securities points out that Friday’s BLS report will include hiring for the government census, which begins in April and could offset some job losses in the private sector.

Prior to the ADP report, economists surveyed by Dow Jones Newswires said the BLS will report April job cuts totaling 610,000, compared with a 663,000 loss in March. Following the ADP data, Nomura Securities revised its estimate of jobs losses to 575,000 from 625,000. High Frequency Economics revised up its forecast to 500,000 job cuts from 650,000.

Joshua Shapiro of MFR Inc. left his forecast for job losses at 600,000, citing the mixed track record of the ADP report as an indicator of the BLS data. In the last four months, ADP has been lower than the official number twice and higher twice. On average, March and February’s initial data from ADP estimated 73,000 more job losses in the private sector than the BLS numbers reported the following Friday. ADP’s April data could indicate a correction following two months of data that were weaker than the BLS figures.

RDQ Economics also didn’t change its forecast for Friday. “We would be more encouraged by the indication of a significant slowing in the pace of employment declines suggested by this report if it was corroborated by other labor market indicators,” RDQ economists said.

Even if Friday’s number surprises to the upside and indicates some stabilization in the labor market, monthly job losses near the half million mark still indicates major economic difficulties. “We remain profoundly skeptical of the idea that the economy is now on a smooth path to recovery,” said Ian Shepherdson of High Frequency Economics. “Those parts which took the biggest pounding after Lehman are rebounding to some degree but the overarching problem of massive household leverage remains.”