There's a very easy way out of this, and it is for the government to (1) recognize and (2) respect that there are going to be objections to contraceptive coverage. You'd think that would be pretty easy. I guarantee if a union made such objections, they would have been recognized and respected. The administration forced this policy upon religious organizations and did not need to. It was very foreseeable that this problem would arise.
I do think there's a difference between the Catholic Church and Hobby Lobby, but I also think that it isn't particularly relevant. If the government had done what it should have and respected that contraceptive coverage shouldn't be mandated, then we aren't even having this debate.
And if anybody thinks single payer is going to solve this, I submit that it will only make things worse in all the ways ObamaCare is failing now. Controversial mandates, underpayment of doctors, death panels debates, etc... ObamaCare is a mini version of single payer.