The argument is pretty simple, really:
1. Businesses are profit-maximizers, and, as such, they hire up until the point that marginal revenue from hiring an additional worker is equal to the marginal cost of hiring that additional worker (i.e., if the increased revenue you'd get from hiring someone is less than the cost of hiring that person, then you won't hire them; if the additional revenue is more than the cost of hiring that person, you'll hire them; if the increased revenue and the increased cost associated with hiring that worker are equal, then you're at equilibrium, and have no reason to hire that worker, either).
2. Obamacare raised the marginal cost of hiring that additional worker, thus causing businesses, all other things being equal, to not only hire less, but possibly to even lay more people off, as the marginal revenue for workers they already had on payroll would likely be below the new marginal cost of keeping them on payroll under Obamacare (caveat: the increased costs associated with Obamacare were not necessarily going to take effect immediately, but the expectation of future cost increases, would still have a deleterious effect, for the same reasons mentioned).
Additional arguments about general regulatory/fiscal uncertainty could be made as well, but I'll just leave it at that.
This chart provides evidence that the above theoretical argument very well may have proven true.