Photographer: Joshua Roberts/Bloomberg

If the CEOs of Fannie Mae and Freddie Mac had big plans for spending the more than six-fold pay raises they got back in July, they may want to reconsider.

On Tuesday, the Senate voted unanimously to approve a bill that would suspend the CEOs' new annual target compensation of $4 million each, capping their pay again at $600,000. In doing so, it would return their compensation to the level set in 2012 following outrage over bonuses paid to executives at the companies, which had been bailed out by taxpayers and were in government conservatorship.

The Federal Housing Finance Agency, which oversees the two mortgage finance firms, approved the new pay arrangements for Freddie Mac CEO Donald Layton and Fannie Mae CEO Timothy Mayopoulos, which were disclosed through the Securities and Exchange Commission in July. The moves would help the companies compete for talent with the private sector, according to reports. In a July statement, FHFA Director Mel Watt said the raises were designed "to promote CEO retention, allow reliable succession planning, and ensure the continuity, efficiency and stability of enterprise operations." An FHFA spokesman declined to comment on the Senate bill for this story.

That bigger pay day seems unlikely to last. The Senate bill will go to the House, and, if it passes, on to President Obama's desk—where he is likely to sign it into law. The White House has objected to the increases, and a similar measure sponsored by Rep. Ed Royce (R-Cal.) passed the House Financial Services Committee by a vote of 57-1.

A spokesman in Royce's office said in an emailed statement that while timing on a vote in the House had not been decided, movement on the issue has been "lightning fast." He noted that "with the almost unanimous support for the bill shown in both chambers, and time sensitive nature of capping these salaries as soon as possible, we could see action as early as mid-October."

The pushback against higher pay for the CEOs of Fannie Mae and Freddie Mac reflects the view that the leaders of government-backed entities should not get the same kind of pay as their peers who run private-sector companies. It also highlights lingering frustration over bonuses that were paid out to executives at these companies amid the financial crisis.

In 2011, headlines blared and lawmakers raised alarms over the big paydays top executives at the two mortgage giants had received in 2009 and 2010. The former CEOs of Fannie and Freddie were awarded approximately $17 million over those two years, much of it in bonuses. That led to a pledge from the FHFA's director in 2012 to cap CEO pay at $600,000. Indeed, Mayopolous, who had been general counsel at Fannie Mae, took a pay cut when he accepted the top job. Layton joined Freddie Mac in 2012.

The new $4 million pay packages disclosed in July were still well below those received by CEOs of the bottom 25 percent of comparable companies. But making those comparisons is inherent to the problem, says Nell Minow, vice chair of ValueEdge Advisers, a governance consulting firm, given the unusual quasi-public nature of the two firms.

"These entities have been duck-billed platypuses from the beginning," she said, noting that the firms need to pay commensurate to the type of organization they're trying to run—and that it's still unclear whether they're ultimately trying to run a private company or a government agency. "This is exactly how anybody who's been watching these two entities from the beginning could have predicted we'd end up."

The focus on the CEOs' pay misses the point, she said. Instead, Congress needs to decide what it wants Fannie Mae's and Freddie Mac's future to look like. "This issue is not how much we're paying these people," she said. "It's what these organizations are supposed to be."

Read also:

This new rule could reveal the huge gap between CEO pay and worker pay

The average S&P 500 CEO makes more than 200 times the median worker

Like On Leadership? Follow us on Facebook and Twitter, and subscribe to our podcast on iTunes.