if he goes with his employer offered healthcare insurance, he is required to go through the exchanges... well, except Congresscritters and their staffers go through a small business exchange in DC that no other federal employees can ( even if they work in DC).
his only other option would be to purchase on the open market and pay about 1000-1500 a month for a plan to cover his family.
taking this option would be indicative of him opposing employer based health insurance, not just Obamacare.. which is not a position he has chimed in on, but it's safe to say he probably isn't opposed to.
at the end of the day, he'll probably go with employer based healthcare insurance...which in the case of federal employees, must be through Obamacare exchanges.
all in all, it's a non-issue... except in terms of political theater.