Solving the problems with the American health care system was never going to be easy, and while I think it's an incontrovertible fact that it sucked and did need radical improvement, it's not obvious to me whether Obamacare has improved things, even on the balance (that there will always be losers and winners is nearly unavoidable with such a change). Many in Europe assume that it must be a good thing because it moves somewhat in the direction of socialized medicine - but it doesn't really, and in this case looking for the middle road is not necessarily a good thing, anyway.
For what it's worth, I think parents here generally pay something like 2000-3000 dollars out of their own purse for births (without complications), though if I'm not mistaken that does include a significantly longer stay in the hospital after birth than in the US (which one might argue is not really strictly necessary in a large majority of cases). Socialized medicine certainly doesn't always mean that the taxpayer funds everything - few countries with socialized medicine would implement something like Medicare. Which brings us back to the American system having some of the worst elements of both worlds. But even among the radical Republicans, few have the guts to take on Medicare frontally...