The truth is something different. As you can see, the issue of part-time employment taking the place of full-time employment became an issue well before the health care legislation ever even become a law.
Despite the obvious evidence that the phenomenon is almost solely attributable to the financial crisis and resulting recession, it hasn't stopped some economists and conservatives from blaming Obamacare (which by the way I don't disagree that Obamacare is being rolled out poorly, but to blame the entire employment situation on it is counter to the evidence):
here and here, for example.
Never-mind the fact that employment numbers have been revised upward and the unemployment rate continues to drop at a steady, albeit slow pace. Consumer confidence continues to rise along with the stock markets. The naysayers still insist that Obamacare is dragging everything down.
And it may yet be true that it might....but the data presently shows that it is the continuing effects of the crisis that are dragging us down. Anyone who suggests otherwise is likely talking more out of politics than economics. Yes, U-6 did tick up ever so slightly (unemployment rate including part-timers that would rather work full-time and discouraged workers) but as I've said before on this blog, you should never take one month's report and assume it is a new trend. It is likely Obamacare will cause a slightly further shift to part time employment but only marginally, and for my money, we should be concerned about the mountain, not the mole hill.