No, our healthcare system is not more broken now. It isn't anymore broken than it was. It merely delayed the inevitable. It did help provide insurance to more people, and it set up exchanges which are at the very heart of competition. The problem is that competition is not a good solution to a complex problem like healthcare.
The ACA was nothing more than the half-measure that was dreamed up by the Heritage Foundation (conservative foundation for those not familiar with it) from 1989 with a few minor updates...all of the key measures (requirement that the same policies are provided to everyone regardless of health status; individual mandate - aka everyone must purchase; and subsidies to keep insurance affordable for lower incomes) were there from the beginning (i.e. all of those components were in the original Heritage plan). The plan was appropriately panned back then as a half-measure that didn't really fix our healthcare system, but Obama figured that since it was the conservative's plan, it would be one of the few things that we could at least start with (which is why it was hilarious that all the Senate Republicans voted against it...it was their own plan). Of course, usual for Republicans, rather than having an actual alternative, they have been busy doing nothing more than trying to just kill the ACA.
So are things worse now than they were before? Absolutely not. Here is the cost of healthcare for various countries around the world as measured by percentage of GDP.
Notice anything? Costs have held steady, relative to GDP, since 2009. Notice something else? We've been going up overall since at least 1980. Remember, this is based on percentage of GDP, so you don't have to worry about inflation. This is the percentage of our economy spent on healthcare. The ACA, if it did anything at all, held it in place for the past few years. It didn't do anything more than that, because it was designed to fix only a few things (the key measures), it wasn't designed to fix the problem of actual costs...or, more accurately, it assumed that competition is magic and that things would magically get better if you forced competition (basically, the same silly beliefs of Libertarians).
Would we have been better off with a single-payer system? Absolutely, that is the secret of all those other countries that have seen their healthcare costs rise only slightly relative to GDP. Unfortunately, the masses have been lied to for so very long that they won't accept such a system. Even if you get mass acceptance, the GOP has relied on it as a wedge issue for so long, they can't go back anymore.