The other day Tim Noah used the occasion of the Senate's vote on allowing any employer to prevent their employees' insurance from covering anything and everything the employer doesn't like (which every Republican senator except Olympia Snowe voted for) to argue that this is yet more evidence that employers ought to get out of the business of providing health coverage, and we ought to just have the government do it. In a single-payer system, these kinds of decisions can be made by our democratic process, and not by every employer individually.
There's just one note I want to make about this. Conservatives have been talking a lot about the importance of preserving the "conscience" of the Catholic Church, their right not to participate in any way in anything that violates their beliefs. That, of course, is a privilege that the rest of us, being citizens of a democracy, don't enjoy. We pay taxes, which go to a lot of things we dislike. I don't like the fact that our government spends as much on the military as every other nation on earth combined. I also don't like the money we spend on tax subsidies for oil companies. My conservative friends don't like the fact that the government gives food stamps to poor people, and pays the EPA to make sure our air and water are clean. But we all pay taxes, because that's how it works—we don't get to pick and choose each line item we want to pay for and which ones we don't.
The Catholic Church, on the other hand, like all religious institutions, doesn't pay taxes. Nor do their affiliated organizations like hospitals and universities, because they are non-profit organizations. So if we had a single-payer system, the Church wouldn't be involved in anybody's insurance. The only way they could influence the law would be the way they do on other issues: not by demanding that the law give them yet more special treatment, but through their moral persuasion on how they think the rest of us should act. And you can imagine how much force that would have.