Since ObamaCare passed in 2010, peak levels of involuntary part-time work have slowly but actually declined from in excess of 9.2 million in 2010 to 9.1 million in 2011, to 8.6 million in 2012, to 8.2 million in 2013.
These levels remain extraordinarily high, but are an after effect of the depression of 2008-2009 and cannot be blamed on ObamaCare. You can blame Obama for not doing anything about it, but you can't really point to ObamaCare as the cause of high levels of part-time employment because those levels have actually declined about 10% since the law was passed. Things might be different had Obama not unilaterally and unlawfully delayed the employer mandate in ObamaCare, but it is what it is, and until the law takes full effect it is not possible to say much more.
There appears to be a lower bound at 7.6 million below which involuntary part-time has so far been unable to fall. If the metric doesn't break that barrier this winter, all it will tell you is that the lingering after effects of the depression are still with us, not that ObamaCare is part-timing the work force.
A real recovery in jobs would put this measure back in the 4 million range where it was before the crisis of 2008 hit, on the assumption that the roughly 4 million extra people in this category who work part-time would be the first to be elevated to full-time when employment conditions improve.