It’s disingenuous to argue that you could increase the number of people who are covered by the healthcare system, maintain people’s access to healthcare, and maintain the average quality without seeing noticeable cost increases without dramatically decreasing the number of preventable illnesses and injuries (and the massive cost associated with bureaucracy).
With that said, I expect the United States will probably "pay for" government run services by rationing services and from the revenue generated from cap-n-trade; and I wouldn't be surprised to see higher taxes introduced on Tobacco, Alcohol and Junk Food.
Edit: Since I want to preempt the claim that there are no problems associated with other Government run healthcare systems around the world, I will just let the statistics I saw earlier today from the government of Saskatchewan do the talking for me. The following website tracks the wait times associated with surgical procedures that are performed after the surgery has been scheduled by a specialist; and, while it is not tracked on this site, the wait time to see a specialist in Canada typically ranges from 1 to 6 months. Please note that a biopsy is considered a seperate surgical procedure, and if a doctor schedules a biopsy the surgical wait time begins after the biopsy is completed.
http://www.sasksurgery.ca/wli-wait-list-info.htm
Just because I was doubted earlier when I suggested that the primary reason why Americans have such better survival rates when it comes to prostate cancer than other nations was because of how efficient and high quality the American healthcare system is. In Saskatchewan only 15% of men can get a Prostatectomy within 6 weeks of it being scheduled, and over 45% wait 4 months or more; and when you factor in wait times for seeing a specialist, and any time associated with diagnostic surgery, this translates to (roughly) 50% of prostate cancer patients waiting 6 months or more for a Prostatectomy. If you're an individual who was unfortunate enough to have your cancer found late it is highly likely that you will die unless you do what so many Canadians do, and that is travel to the United States and pay for healthcare to save your life.