The problem with the laws is the majority of people who are actually going to sign up for insurance are the people who couldn't get it before because of pre-existing conditions. These people are often a strain on insurance companies and they are balanced out by the healthy young people who cost very little. However, those young people are currently foregoing insurance entirely and thus the health care companies will have to raise prices in order to balance out costs.
Universal health care is something that will never be truly realized because it is so expensive to pay every ones medical bills without bankrupting yourself. Government mandated health insurance is an economic burden to the United States due to the inefficiencies in the healthcare system (i.e. drug abuse, recidivism, addiction, relapse).
It is already happening. People have to pay more in order to keep the same insurance coverage they used to have. I personally know such people. Some of them posted rants on Facebook, others spoke about it in person. And it's not just a little increase: it's around $400 per month more to pay.
If anything, health insurance will be cheaper because there is now greater demand and supply for health insurance coverage. The more people who have coverage, the more money there is available for health insurance companies to invest. The more investment capital they have, the more money health insurance companies make. When the customer base increases for insurers, more products are available and prices go down.