It looks like investors aren’t worried about the uncertain future of healthcare reimbursements.

Reuters is reporting that hospital chain HCA HCA is expected to raise over $3.7 billion in its IPO, by pricing 124 million shares at the high end of its $27 to $30 per share offering range. Nothing official yet, however, and this follows an earlier Reuters report that the pricing could approach $31 per share.

[Update: The company priced 126.2 million shares at $30 a piece, raising $3.79 billion]

Either way, HCA’s success — it will be the largest private equity-backed IPO in history — is coming against some pretty serious odds. Conventional wisdom in the capital markets right now is that healthcare providers are to be sold, not bought.

“The only part of healthcare we’re touching right now are back-end services,” explained a private equity investor with several healthcare investments. “There is way too much uncertainty in anything that requires government reimbursement.”

When healthcare reform legislation first passed, many investors began to salivate over the millions of newly-insured customers. But then folks began worrying about cost controls, plus the prospect of the legislation being either repealed or ruled unconstitutional. Add to that a bubbling debate over entitlement reform, and companies like HCA look quite vulnerable. After all, 40.7% of the company’s 2010 revenue derived from Medicare and Medicaid.

As HCA explains in its prospectus:

“Changes in government health care programs may reduce the reimbursement we receive and could adversely affect our business and results of operations… Current or future health care reform efforts, changes in laws or regulations regarding government health care programs, other changes in the administration of government health care programs and changes to commercial third-party payers in response to health care reform and other changes to government health care programs could have a material, adverse effect on our financial position and results of operations.”

But none of this apparently bothers those who have spoken for around $3.7 billion worth of HCA shares.

Only time will tell if it’s a smart bet, but I’m certain that owners of other privately-held healthcare services providers will watch the HCA after-market very closely. After all, most of them still think that now is the time to sell.

“You have a lot of other PE-backed hospitals companies like Vanguard, IASIS and Capella that have been waiting for this to happen,” says a healthcare investment banker. “HCA is considered the Cadillac and, now that it’s priced, others probably will try to slot in right behind them.”

HCA was taken private for $33 billion in November 2006 by Kohlberg Kravis Roberts & Co. KKR , Bain Capital and Merrill Lynch Private Equity. Its IPO underwriters include BoA Merrill Lynch BAC , Citi C and J.P. Morgan JPM .