Key Senate negotiators were still grappling Thursday with how to limit the scope of a Treasury Department plan to backstop Fannie Mae and Freddie Mac.

With the two mortgage giants facing a crisis of confidence in the markets, Treasury Secretary Henry M. Paulson Jr. has spearheaded a plan to extend new credit lines to the companies and allow the government to buy stock in them, if such steps become necessary. Paulson has made the congressional rounds this week in an effort to drum up support.

But several lawmakers, primarily Republicans, have expressed concerns about handing a “blank check” to Treasury. The Treasury proposal does not include an upper limit on the credit line or its power to purchase equity stakes in the companies, though the authority would expire at the end of 2009.

“I’d rather something be finite,” said Richard C. Shelby, the ranking Republican on the Senate Banking, Housing and Urban Affairs Committee. In the closely divided Senate, Shelby’s support is often essential for moving major financial legislation.

Chairman Christopher J. Dodd., D-Conn., said negotiators are trying to work out a compromise that satisfies both Shelby and other critics and the Treasury, although he sounded somewhat frustrated at the challenge.

“How do you give some definition to something like that, where your goal is ambiguity and you’re looking for some definition? It’s inherently conflicted,” he said.

Shelby said he understood the need for “ambiguity” in the Treasury’s proposal, given the jitters of investors. Paulson has argued that granting broad powers to Treasury would go further to increase market confidence than narrow, circumscribed authority — making it less likely the powers would ever have to be invoked.

But Shelby, along with many other Republicans, fret that taxpayers could be exposed to some portion of Fannie and Freddie’s $5.2 trillion in outstanding debt and obligations.