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Small businesses are still having a hard time finding workers despite recent indicators showing that the employment picture is getting better.

In the latest National Federation of Independent Business survey, the portion of small business owners who say they are unable to fill jobs rose to 21 percent from 18 percent. A third of them say that have few or no qualified applicants for openings.

The news is at least a bit of a counterweight to the most recent government employment report, which said the economy created 236,000 jobs in February as the unemployment rate fell to 7.7 percent.

Read More: US Job Creation Surges as Rate Falls to 7.7%

"A large portion of the current supply is likely folks that were displaced in the aftermath of the housing bubble. These are jobs that will return at a glacial pace," RBC Capital Markets said in a report. "This is all part and parcel of the structural repair taking place in the housing market."

Pairing up workers with available jobs has been one of the biggest obstacles in getting unemployment down.

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While the headline rate has fallen, it has largely resulted from discouraged workers leaving the labor force, which is at a three-decade high. The principal unemployment rate includes only those unemployed who are looking for jobs. A broader gauge that measures discouraged and underemployed workers remains elevated at 14.3 percent.

The Federal Reserve is tying monetary policy to the headline unemployment rate and said it will not start raising interest rates until joblessness falls to 6.5 percent.

Read More: Want the Fed to Tighten? Don't Hold Your Breath

"What is important about this debate is that if most of what's holding back a faster improvement in the unemployment rate is structural in nature — i.e., a skills mismatch that will only be corrected via retraining of the workforce and/or the gradual improvement in the housing market—then the Fed is ill-equipped to deal with this problem," RBC said. "No amount of quantitative easing will make the gargantuan amount of unskilled labor supply more employable."

Consequently, the jobs picture is likely to remain muddy.

For all the optimism of the government's report Friday, there were other weaknesses in the data.

More than 100,000 of the new positions came through the Labor Department's Birth/Death Model, which approximates the number of positions created through new business creation and failure.

Read More: Consumers Still Strong, Just Keep on Spending

The Job Openings and Labor Turnover Survey, also from the government, showed a net of 145,000 new positions filled, which is at or just below the level associated with bringing down the unemployment rate.

Market research firm TrimTabs said its independent count, which relies on income tax withholdings, showed just 100,000 new jobs.

"The U.S. economy is not as strong as the conventional wisdom believes." said TrimTabs CEO David Santschi.