What do you do when the opposition’s working night and day to convince voters that you’re an obstructionist, almost nihilistic group that’ll never compromise on anything? Raise the stakes and catch them off guard by proposing a much bigger compromise than they were expecting.

Just one problem with this offer: Would the public really view Obama as the unreasonable party to these negotiations if he turned around and said no?

With the administration’s debt ceiling deadline fast approaching, House Republican leaders are considering a four-year debt limit increase that would take the issue off the table for the rest of President Barack Obama’s presidency.

The plan would, however, come at no easy price for Obama, who pledged as recently as Monday morning not to negotiate with Republicans on a debt ceiling hike. Republicans would demand major tax and entitlement changes — the latter of which has been anathema to many Democrats — and they could also ask for movement on the sequester and an expiring continuing resolution that must be dealt with in the next three months.

The idea was one of many brought up over Sunday and Monday, as Speaker John A. Boehner of Ohio and his leadership team and staff held a strategy session in Warrenton, Va.

“We have an opportunity to inject years of certainty while doing some fundamental tax reform and entitlement reform,” said Rep. Steve Southerland II of Florida, the sophomore class leadership representative, who was at the meeting.

Unless the GOP’s prepared to not only hit the ceiling but hold out for weeks under immense economic and political pressure in hopes of extracting major cuts (which seems unlikely if even Republican senators are grumbling about another debt limit standoff), then a big PR ploy like this makes some sense. If you’re not going get anything meaningful from a confrontation, why not use it as an opportunity to make the left into the bad guy? Four-year debt-ceiling increase! Party of yes! New golden age of bipartisan cooperation! If the Democrats can come to the table, of course.

Let’s game this out, though. Boehner calls a press conference, walks out to the podium, and declares that the end of manufactured budget standoffs must end. The solution: A massive debt-ceiling hike to cover the rest of O’s presidency in exchange for reforms to Social Security and Medicare. Obama then calls a presser of his own, walks out, and says, “Sounds interesting! Name the cuts you have in mind.” So Boehner huddles with Cantor, Kevin McCarthy, and Paul Ryan, calls another presser, and lists all sorts of cuts and reforms to entitlements that’ll slash the deficit. Whereupon O calls his second presser and declares that he’d never, never abandon America’s seniors by agreeing to the sort of draconian cuts that the GOP so cruelly blah blah blah blah. What’s Boehner’s move then? The political damage has already been done at that point; Democrats will spend the next two years Mediscaring ahead of the midterms. Instead of being demagogued in the media as spiteful obstructionists who want America’s credit rating to implode, they’ll be demagogued as vicious misers looking to balance the budget on grandma’s back. What Boehner could do to prevent that is refuse to name any specific cuts publicly and insist that they be negotiated between the parties behind closed doors. But Obama won’t go for that; he won’t give away his Mediscaring opportunity, so he’ll simply turn around and say, “Get back to me when you’ve got something concrete in mind.” What then?

The only way the GOP has real leverage in negotiations against a Democratic president and Senate is if they have the public on their side, but the whole point of the last election is that the public’s even less serious about fiscal reality than the Democrats are. That’s been said many times in media old and new lately, but it can’t be said enough. When you poll people on their policy priorities, deficit reduction always does well, but once you drill down to bedrock stuff like entitlements voters start to abandon ship. What’s the GOP supposed to do in those circumstances? They can’t shut down the government to force spending cuts because the public hates shutdowns. They can’t offer a major compromise like a four-year debt-ceiling hike to encourage cuts because the public hates the sort of cuts that would be needed to really drive down the deficit. The only thing that could move public opinion is a sustained bully-pulpit educational campaign by the White House, but there’s zero reason to think Obama’s interested in that. As Philip Klein notes at the Examiner today, The One has never agreed to spending cuts unless a crisis has forced him to. So again: What do you want Republicans to do? Even if they went full kamikaze and won some cuts by enforcing a sustained federal shutdown, they’d face a huge risk of being swept away in a backlash in the midterms and those cuts being rescinded by the new Democratic House. The problem isn’t that the House leadership “has no balls” or whatever, it’s that they have no partner on fiscal responsibility. Not even in the electorate.