Weekly unemployment insurance claims fell in the week ending April 5, the Department of Labor reported Thursday, to 300,000 -- the lowest number since early 2007, well before the beginning of the recession. The four-week moving average for claims also fell to 136,250, the lowest post-crisis level, setting aside a stretch last fall when California failed to report its claims.

Because unemployment benefit claims are a leading indicator, the better-than-expected number could be taken as an indication that long-tepid U.S. job growth is finally poised to break out.

Especially following Friday's relatively strong March jobs report, it is a good sign that fewer Americans are being laid off or fired since before the financial crisis, but it is no guarantee that monthly jobs gains will quickly break through the roughly 180,000-200,000 band they have fallen into since 2010.

That is because the major impediment to job growth right now is hiring, not firing.

In fact, the rate of layoffs and discharges, which lead to workers taking up unemployment insurance, first fell to normal non-recession levels in early 2012. The rate, as reported by the Bureau of Labor Statistics, fell to its lowest level as a percentage of total employment, 1.1 percent, last fall, before rising to 1.2 percent again.

But hiring still remains depressed. At 4.6 million in February, monthly hires are still 500,000 to 800,000 below their pre-recession levels. Job openings have recovered slightly more quickly, but businesses haven't been able to find workers as fast as they can create jobs.

"Pretty clearly the number of firings is moving as low as they can go," noted BTIG strategist Dan Greenhaus on Twitter. Nevertheless, businesses will have to continue creating positions and then finding workers to fill them for the labor market to really pick up.