It is unclear how much U.S. taxpayers will eventually have to shell out to help mortgage finance giants Fannie Mae and Freddie Mac, the regulator of the two companies says.

"The actual cost I do not know," Federal Housing Finance Agency Acting Director Edward DeMarco said in response to a question from Kentucky Republican Senator Jim Bunning at a Senate Finance Committee hearing.

Fannie Mae said this week it would need an additional $8.4 billion from the U.S. Treasury. The two firms have now tapped about $145 billion from the government and the Obama administration has said it will backstop losses, no matter how high they go, through 2012.

As a result, some Republican lawmakers are pushing for Fannie Mae and Freddie Mac to be included among firms subject to a tax aimed at financial institutions that received government money during the financial crisis.

Congress approved $700 billion in late 2008 for the Troubled Asset Relief Program (TARP), often referred to as the bank bailout.

Many financial institutions have repaid their TARP commitments, and losses from TARP are now estimated to be around $90 billion. The proposed fee is designed to get that money back.

While Fannie Mae and Freddie Mac did not receive TARP funds, then Treasury Secretary Henry Paulson took control of the two firms in late 2008 as losses from risky mortgages mounted.

Under the terms of the government "conservatorship," the firms have access to a separate, unlimited credit line from Treasury to backstop their losses.

DeMarco pointed out this week that any tax paid to the Treasury from Fannie and Freddie would ultimately come from the Treasury itself.

"To assess a particular fee at this time to Fannie and Freddie would not accomplish anything in terms of increasing revenue to the government," DeMarco told the lawmakers.

David John, a senior research fellow at the conservative Heritage Foundation in Washington, said he would like "nothing more" than to privatize Fannie Mae and Freddie Mac and shrink them as much possible.

But imposing a tax on them does not make sense because "it would make little sense to tax what is effectively another arm of the government," John told the panel, echoing DeMarco's remarks.