Completely false. Even the Democratic Senate that produced the healthcare bill found that only 15-20% of healthcare costs related to the overhead and profit of the insurance companies.
Note that just because those politicians are Democrats, that doesn't mean that they aren't in the pocket of Big Pharma, Big Insurance, and Big Healthcare and that they thus weren't motivated to try to make the numbers look more favorable for them. (Our politicians know where their bread is buttered.)
There are three major reasons that health care is more expensive in the US than other places. We receive more and higher quality healthcare, we live a less healthy lifestyle, and doctors here make far more money than in countries with single payer systems.
It feels better to go after the insurance companies than the doctors but if you put your feelings aside and look at the numbers it's clear where the money is going.
Do you really think it's the doctors, many of whom only make around $150,000-200,000/year while having to pay off large student loans (with mostly after-tax money), who are the problem? My wife had some major surgery a couple years ago and the total cost was about $21,000. The surgeon's portion was only about $1500 of that.
Also, the administrative costs are not just in the form of insurance companies, but in all of the other people who don't have anything to do with the actual provision of health care (all non-nurses, non-doctors, and non-technicians, etc.). The people who handle the billing and the front-line screeners who make sure that you have the proper health insurance, etc., are a part of the cost. Health insurance brokers are part of the cost. Company benefits plan managers in HR are part of the cost. Hospital and (prescription-based) pharmaceutical advertising is part of that cost.
I wouldn't be at all surprised if 40-50% of all the people whose income comes from providing health care have nothing at all to do with the actual provision of health care.