All those companies that offered health insurance before Obamacare still provide it
As with our previous paper, we found no evidence that ESI offer, take-up, and coverage rates fell from June 2013 to March 2015 overall for workers below 250 percent of FPL or for workers in in small firms. These results likely reflect the effects of the individual mandate as well as strong tax incentives to obtain coverage from employers. Because of those tax incentives, most workers are financially better-off if they obtain coverage through employment. Consequently, employers now have increased incentives to maintain their offers for coverage and workers have increased incentives to take up that coverage when it is available. The ACA’s employer mandate for large firms, when it is implemented, should add to these incentives, though as shown in figure 1, offer rates in large firms are already well over 90 percent.That's academic-ese for saying that employers were offering insurance before Obamacare, and employees were accepting it and keeping it. After Obamacare, all of those things remain true and essentially unchanged, and every study that's been done before says the same thing.These findings are consistent with the findings of several microsimulation studies conducted before the ACA and with experiences in Massachusetts under its 2006 reform initiative. For example, the Congressional Budget Office predicted only a small decline in ESI: 6 million by 2016, or a reduction of 3.7 percent, out of 161 million people that would have had coverage without the ACA in 2016. RAND estimated that, relative to a no-reform scenario, the ACA would lead to a net increase of 8.0 million people with ESI (Eibner et al. 2010). Other microsimulation models—for example, that of the Lewin Group (2010) and the Urban Institute (Blumberg et al. 2012)—predict changes in overall ESI within the range of the Congressional Budget Office’s and RAND’s estimates. Finally, experience from Massachusetts suggests that an individual mandate along with a relatively weak employer mandate actually increased the rate of ESI coverage (Gabel et al. 2008). Other early estimates of ESI changes under the ACA from Gallup and RAND surveys also find ESI is holding steady (Levy 2015) or increasing (Carman and Eibner 2015) among the nonelderly population. Thus, findings to date all suggest that ESI should stay relatively stable under the ACA.
But we know that facts have a liberal bias and reality is not a place in which Republicans care to exist, so don't expect them to stop parroting the old line about how employers are going to take people's health insurance away.