Right now, most of the problems with Obamacare's online insurance exchanges are with the signup process, particularly in the 36 exchanges being run by the federal government. But there are deeper, more fundamental problems looming even if the surface web-accessibility problems are largely fixed.
For example: Just because someone has completed the online enrollment process doesn't mean that they've actually gotten coverage. Reports indicate that many of the applications that are making it through the system don't actually have enough data for insurers to process the enrollee.
"Rightful liberty is unobstructed action according to our will within limits drawn around us by the equal rights of others. I do not add 'within the limits of the law' because law is often but the tyrant's will, and always so when it violates the rights of the individual." Thomas Jefferson
"If people can’t trust not only the executive branch but also don’t trust Congress, and don’t trust federal judges, to make sure that we’re abiding by the Constitution with due process and rule of law, then we’re going to have some problems here." - Barack Obama, June 7, 2013