(FORTUNE Magazine) – FOR TWO YEARS EVERYONE FROM Washington to Wall Street has argued that Congress needs to pass legislation creating a strong new regulator for Fannie Mae and Freddie Mac. Now would seem to be the time, largely because the mortgage giants' awesome political power, which once made them all but impervious to criticism, has been blunted by multibillion-dollar accounting scandals. Indeed, on May 25, legislation authored by Representative Richard Baker (R-Louisiana), a longtime critic of Fannie and Freddie, passed the House Financial Services Committee with a resounding vote.

But today the Baker bill seems to be in trouble--and some observers say it's possible that yet another year will pass without any new legislation. What's the explanation? It starts with Fannie and Freddie's opponents, who believe the Baker legislation doesn't go far enough. Of late, the most vociferous public critic has been Fed Chairman Alan Greenspan. In early 2005, Greenspan testified that he thought the companies should be forced to sell off most of the $1.5 trillion in mortgages on their books. Since then, he has been a broken record about, as he put it in a recent speech, the "significant systemic risks for our financial system" that the portfolios may pose, in essence because mortgages are very sensitive to swings in interest rates. (Greenspan also argued that while the portfolios contribute to Fannie and Freddie's bottom lines, they do nothing to reduce mortgage rates.) Today, the Fed's view--which Bush's Treasury Department has endorsed-- is that any legislation must limit the size of Fannie and Freddie's portfolios. This concept, of course, is anathema to the companies, in part because it would reduce their profits.

But both Baker's bill and the reaction to it make it crystal clear that Congress is still hesitant to reshape Fannie and Freddie. The bill is missing the strict portfolio limits Greenspan wants. Baker argues his legislation contains provisions--such as one that allows Fannie or Freddie to be placed into receivership should either fail--that he says "would have once been unthinkable." And Freddie CEO Dick Syron has characterized the bill as "very tough."

But critics vehemently disagree. The American Enterprise Institute, which wants Fannie and Freddie privatized, wrote that a bill that was supposed to create a "'world-class regulator' is in fact a world-class failure." Among the provisions that have provoked the ire: one that would allow Fannie and Freddie to buy larger mortgages than they can now, thereby increasing their ability to grow.

Despite the massive accounting scandals at both companies, which drove CEO Franklin Raines from his job last December, Fannie and Freddie still have plenty of friends in Congress. At a recent hearing, Senator Chuck Schumer (D-New York) praised them for having "done a very, very good job." The truth is, Fannie and Freddie don't even have to lobby. Members of Congress are terrified (with good reason, perhaps) that by reining in Fannie and Freddie, they could get the blame for pricking the housing bubble. And traditional allies of the companies, such as the homebuilders and the realtors, can pick up any lobbying slack while Fannie and Freddie lie low. This is partly why analyst Josh Rosner of Medley Global Advisors, an independent research firm, says, "There is less chance of hard limits than of Pee-wee Herman becoming President."

Indeed, an institutional-investor conference call held by Prudential Securities after the Baker bill was passed suggested that Fannie and Freddie partisans were ready to pop champagne corks. One consultant, Terry Haines, noted that the Baker bill was "hard evidence for the first time" that the administration's views were "marginal." He went on to criticize the White House for being "shrill" and "late to the party," and he essentially dismissed Greenspan by saying that "the Fed is not exactly the housing regulator." Consultant Howard Glaser noted that another provision in the Baker bill, which requires that the companies devote 5% of their earnings to providing affordable housing, "creates real political power" for the companies. (Glaser now says he wasn't expressing his own views, he was merely explaining why critics fear the provision.) The call was in effect a victory lap, and publicly many of the bill's supporters say the Baker legislation is on track to be signed into law.

But the victory lap may turn out to be premature. Fannie and Freddie's opponents are far from powerless, and conservative hatred of the affordable-housing provision has provided an easy way to derail the legislation, at least for now. This puts Fannie and Freddie in an awkward spot. They actually want new legislation because it will remove the uncertainty about their prospects on Wall Street. The situation also presents a risk for Fannie opponents who are hoping for tougher legislation in the future: If Fannie and Freddie are still strong today in the immediate aftermath of the accounting scandals, won't they only get stronger as the memory fades? -- Bethany McLean