Bain, which late last year started gauging investor interest for a new buyout fund, relied on pensions for about 9 percent of client assets in a recent fund. The firm has traditionally raised most of its capital from foundations, endowments, family offices and wealthy individuals.

Alex Stanton, a spokesman for Bain Capital, declined to comment.

When Romney set out to raise Bain's first fund in 1984, he steered clear of pension funds, pursuing ultra-high net worth individuals who contributed about $37 million to form the fund, according to a person who worked with Romney at the time. KKR's co-founders, by contrast, received early capital from Oregon's and Washington's pensions, with the latter contributing $12 million to KKR's first fund in 1982.

The success of Bain's first fund, which generated a 61 percent average annual return, according to marketing documents from 2004 obtained by Bloomberg News, helped attract other investors who wanted to share in the profits and allowed Bain to charge a premium for its investment services. The firm collects 30 percent of the profits it earns on its investments, the highest in the industry. Pensions historically have been less willing to pay Bain the higher performance fees.

With Romney keeping the spotlight on Bain, public plans may be reticent to invest now because of the controversy, said Heather L. Slavkin, senior legal and policy adviser for the office of investment at AFL-CIO, the nation's largest union federation.

"Trustees are concerned about headline risk and there's a headline on Bain every day," said Slavkin, whose office advocates for the security of $480 billion of union-sponsored pensions. "Nobody wants their decisions under a microscope and trustees are no different. They don't want to see their decisions questioned publicly."

For their part, many firms say the firestorm will blow over and pensions will come to rely more on private equity to meet their growing obligations to workers because traditional assets like stocks and bonds won't return enough.

The Federal Reserve this month said it would keep interest rates low through 2014, driving investors into higher-yielding assets and pushing down borrowing costs for leveraged buyouts.

Bain Capital Managing Director Stephen Pagliuca, also speaking in Davos, said investors will stick with the firm and criticism of the private-equity industry will pass.

"Our limited partners have been with us for 28 years many of them," he said in an interview with Erik Schatzker. "We just keep our heads down and try to build value."