As negotiations on raising the debt ceiling go down to the wire and with no clear endgame in sight, the White House finds itself again tamping down suggestions by some Democrats on Capitol Hill that it invoke the 14th Amendment and raise the country’s borrowing limit without congressional approval.

From a political perspective, the 14th Amendment route would be an unprecedented one fraught with peril, as The Post’s Aaron Blake has detailed.

But the case could also be made that a congressional stalemate — followed by a unilateral move by the White House to prevent default — could present the best-case scenario for the president’s political fortunes.

Here’s a look at some of the possibilities if the debt-ceiling negotiations fail to produce a result.

Polls show Americans’ approval of Congress at only 18 percent, not far from its all-time low of 13 percent in December.

Obama’s approval has hit a new low, but it still remains more than double that of Congress, at 40 percent.

Leaders on Capitol Hill are united in their insistence that they do not see default as an option, a point reiterated by House Speaker John Boehner (R-Ohio) and Senate Minority Leader Mitch McConnell (R-Ky.) at a Saturday afternoon news conference.

Still, the path toward a compromise that can win passage in both chambers remains unclear, and the default deadline is just three days away. If the deadline were to loom with a deal not yet sealed, Obama could move to raise the debt ceiling on his own, casting himself as the “adult” in the room and making the case that Congress has become so paralyzed by partisanship that it has put the full faith and credit of the country at risk.

At that point, the biggest political questions would be: How would the public react? What would the parties do? And what action would the White House take?

Public reaction would hinge on the views Americans already hold of Congress and the White House. In Washington, each party has been preparing for weeks to blame the other for a potential default — and the finger-pointing would be certain to continue post-Aug. 2.

But outside the Beltway, polls show that views of who’s to blame would be mixed.

A failure by Congress to pass a deal would be likely to reflect poorly on the institution as a whole — an institution that, it’s worth bearing in mind, has been unable to resolve even the minor impasse that has led 4,000 workers to be furloughed in a partial shutdown of the Federal Aviation Administration. That standoff is now entering its second week.

The public’s response to a 14th Amendment move by the White House would also depend on the reactions of the political parties, both on and off Capitol Hill.

For Democrats, the question would be whether they would continue to work with Republicans on addressing the broader debt problem.

Democrats have already been giving Obama wiggle room on the 14th Amendment option by floating the idea as the debt deadline nears, and former president Bill Clinton gave Obama perhaps his most significant political cover when he said earlier this month that if he were the one in the White House, he would go ahead and raise the debt ceiling.

But if, after such a move, congressional Democrats abandoned any effort to tackle the country’s debt, they — as well as the White House — could face dire political consequences, as they would essentially be giving their blessing to a multitrillion-dollar hike in federal borrowing without any spending reforms.

For Republicans, the main question would be whether to seek to impeach Obama. Republicans would also face the choice of whether to focus on the constitutional argument (that Obama overstepped his executive authority), the reckless-spending argument (that Democrats are not serious about getting the country’s fiscal house in order) or perhaps both.

A move to impeach Obama would lead to a months-long political circus, the result of which is unpredictable. It could wind up either a benefit for Republicans (an opportunity to put the White House in the hot seat in the leadup to November 2012) or for Democrats (the effort could backfire among a public weary of partisan politics and concerned about the state of the economy).

The constitutional argument might serve to rally the Republican base — just as the congressional debate over Libya has most energized not moderate lawmakers but those on the far left and right.

But Congress’s response to the Libya debacle has also diluted somewhat both chambers’ ability to effectively challenge Obama’s executive authority. The House has given mixed message after mixed message on whether Obama should have consulted Congress on Libya, while the Senate has yet to take up a resolution on the matter at all since Obama committed U.S. troops to the conflict.

Add to that the fact that most Americans are concerned about the economy and not separation-of-powers issues, and it could make for a tough sell to the public at large.

On the spending issue, a unilateral debt-ceiling increase by Obama without any corresponding spending reforms would undercut Democrats’ message that they are serious about setting the country’s finances in order. That would be a net win for Republicans — especially those on the 2012 campaign trail.

That’s where the White House’s actions following up a 14th Amendment move would be key. A move to raise the debt ceiling through the end of 2012 would be less politically perilous if it were coupled with a serious attempt to create a deficit-reduction framework. But it wouldn’t be entirely without risk. And such a move would put the ball back in the court of congressional Republicans, who could argue that the White House’s move to raise the debt ceiling first and address spending reforms later reveals its priorities when it comes to fiscal responsibility.

What are your thoughts? Who would benefit politically from a 14th Amendment move by the White House? The comments section awaits!