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The U.S. Chamber of Commerce may sue the Obama administration over President Obama's controversial appointment of Richard Cordray to head a controversial consumer financial board, officials from the business group told Fox News on Wednesday after an unprecedented display of executive power that is sure to poison already-strained relations with the GOP.

Chamber spokeswoman Blair Latoff and colleague Bryan Goettel both told Fox News that their understanding is that "we are not ruling it out." However, they said they still "need to understand the specifics of the appointment to determine if a legal challenge is even possible."

The chamber was early in its criticism of the president's move Wednesday to appoint Cordray to chair the Consumer Financial Protection Bureau in a move that invites legal challenge but which administration officials say is perfectly within the president's authority to do.

"To say we are disappointed in the move by the president today would be a gross understatement," Chamber President Tom Donohue said in statement. "This controversial appointment is unprecedented, constitutionally questionable, and puts the authority of the director and the validity of the bureau’s work in legal jeopardy. What's more, it ignores repeated calls to reform the bureau by restoring basic checks and balances."

Others are also questioning the validity of the president's move. Senate Minority Leader Mitch McConnell, R-Ky., who could become the majority leader in 2012, released an ominous statement Wednesday, saying the appointment "lands this nominee in uncertain legal territory, threatens the confirmation process and fundamentally endangers the Congress' role in providing a check on the excesses of the executive branch."

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One senior GOP aide told Fox News to expect a lawsuit from an outside group that would fall under CFPB's regulatory jurisdiction since Congress itself would lack the authority to sue.

"It's our understanding that someone affected by the CFPB would have standing here, not the House," another aide told Fox Business Network. "So some business that gets clobbered by the agency could sue."

The GOP aide added that aside from an almost immediate challenge, even if Cordray moves into the post, he will face a wall of opposition at every turn.

Cordray "will get absolutely nothing done. Also, funding (for the CFPB) will be in some peril," the aide said.

The White House might not mind a fight during a presidential campaign year, as Obama looks to frame the battle as one against obstructionist congressional Republicans who are against middle-class Americans.

"I nominated Richard for this job last summer, so you may be wondering why am I appointing him today," Obama told supporters in Ohio, where Cordray appeared with him in Shaker Heights. "It would be a good question. ... The only reason Republicans in the Senate have blocked Richard is because they don't agree with the law that set up a consumer watchdog in the first place. They want to weaken the law. They want to water it down."

Republicans made clear both during Cordray's nomination and on Wednesday that they have no problem with Cordray personally, but want changes in the massive new watchdog agency, including a budget and nominee subject to congressional oversight and other reforms in its wide-ranging rule-making authority.

"The president should stop allowing his Chicago political campaign to make his Washington policy decisions," Rep. Patrick McHenry, R-N.C., chairman of the Oversight Subcommittee on TARP, Financial Services and Bailouts of Public and Private Programs, said Wednesday in a statement in which he criticized Obama's claims of transparency in his administration. McHenry also invited Cordray to appear on Jan. 24 before his committee to answer questions about how he would implement policies as head of CFPB.

"There are legitimate policy concerns about the structure of the CFPB. They can be reconciled, but the president refuses to even have the conversation," he said.

Cordray, who was successfully filibustered by Republicans last year, will remain in the job until Jan. 3, 2014, unless confirmed by the Senate sooner, an unlikely event given the current partisan move by the White House.

While controversial, nowhere in the Constitution is a recess expressly defined, though the document does give the chief executive the "power to fill up vacancies that may happen during the recess of the Senate."

As a result, a loose understanding has arisen over the years as to what constitutes a recess.

Most, including Obama's own acting solicitor general, appear to hold to a three-day minimum for a recess, arising from the congressional adjournment clause in the Constitution which states that no chamber may break for longer than three days without the approval of the other chamber.

In a 2010 Supreme Court case, "New Process Steel vs. National Labor Relations Board," acting Solicitor General Neal Katyal referenced the three-day minimum, during which no recess appointment could be made and cited a Department of Justice brief issued in 1993 by Attorney General Janet Reno.

But the document is vague.

In the brief, which was used to argue against a controversial recess appointment by former President George H.W. Bush, Reno called the three-day recess a "requirement." But it went on to say "the Constitution provides no basis for limiting the recess to a specific number of days."

That does not negate the understanding that appears to have arisen in modern times among members of Congress, Democrat and Republican alike. Democrats in 2008 held the Senate in "pro forma" session to block recess appointments by President George W. Bush. At the time, Obama and Vice President Joe Biden, while serving in the Senate, strenuously argued against such an exercise of presidential power.

When Bush appointed John Bolton as ambassador to the United Nations, then-Sen. Obama said the nominee was, as a result of the temporary position, "damaged goods." Noting the Senate had rejected the nominee -- though unlike Cordray, Bolton faced bipartisan opposition -- the senator said the U.S. would have "less credibility" at the world body.

At a Foreign Relations Committee hearing, Biden said, "No president is entitled to the appointment of anyone he nominates," adding, "That's why they wrote the Constitution the way they did. It says 'advice and consent.'"

According to a Congressional Research Service report, since the administration of President Ronald Reagan, no recess appointment has been bestowed upon a nominee during a recess that was shorter than 10 days.

Nonetheless, a senior administration official told Fox News that the White House is on solid ground with the maneuver.

"They're not in session," the official said of the Senate, noting that the Senate has stated that "that no business shall be conducted during pro forma sessions" and the Senate "is unable to receive appointments" during that time because it is not prepared, regardless of the length of time in between, to conduct business during those meetings.

Thus, it is the interpretation of the White House that the Senate is in fact "in recess" and the administration can make appointments.

Despite the predicted fight over the CFPB nominee, one congressional GOP source predicted the fight will have no effect. The aide sited polls that, according to the source, show Americans disinterested in the watchdog agency, with few knowing about Cordray.

"It's just not a 'top of mind' issue. It's nowhere on the radar of anyone," the aide said.

Fox News' Chad Pergram contributed to this report.