President Barack Obama (Jewel Samad/Getty Images)

(The Root) β€” Given that they spent their August recess bragging that they'd oppose Obamacare at all costs, you'd think House Republicans would take ownership of the government shutdown.

But maybe they're not all that proud of it, because after the shutdown's first full day, they pushed back on President Barack Obama's assertion that it's a "Republican shutdown" and argued that Obama β€” not the Grand Old Party β€” is who the public should blame for the gridlock.

Take House Speaker John Boehner, who wrote in a USA Today op-ed that the president "refuses to even talk" to Republicans about a bipartisan agreement. Or Sen. Mark Kirk β€” who holds the same Illinois seat that Obama held β€” who claims that the president's budget-negotiation stance amounts to having a "temper tantrum." And then there's former House Speaker Newt Gingrich, who appeared on The 700 Club Tuesday, telling host Pat Robertson that "President Obama refuses to behave like an American president" and "refuses to deal with the Congress as his equal."

Republicans say they're the ones who have offered the "compromise" of only further delaying, not totally defunding, Obamacare β€” which is, if you think about it, like promising that "they won't break Obama's legs; they'll only break one of his thumbs."

Wednesday night, Boehner will be at the White House for the first of several likely sit-downs with the president and other congressional leaders.

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And although they'll eventually have to hammer out an agreement, Republicans' charge right now that Obama can't work with them doesn't hold up against the events of his presidency. He's tried, repeatedly, to offer concessions to the GOP leadership, to the point where he frequently doesn't satisfy either congressional Republicans or fellow Democrats.

Don't forget that Obamacare β€” whether or not you support it β€” and its individual-coverage mandate were modeled after Mitt Romney's Massachusetts coverage plan. And although candidate Obama ran against the mandate in 2008, President Obama changed course and settled on it when he couldn't find enough congressional support for the then-infamous "public option" that progressive Democrats were pushing for.

There was the 2011 debt-ceiling fight, when Obama and Democrats made the last-ditch offer of across-the-board cuts in the "sequester" to avoid going over the "fiscal cliff."

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And when Obama was prepared to order missile strikes in Syria, he wound up β€” wisely β€” reconsidering his go-it-alone posture, after members of Congress wrote a letter asking him not to bypass their role, and to let them "share the burden" of deciding to go to war.

Of course, Obama did strike a deal with Republicans after they won the House in 2010, when the GOP got an extension of the Bush-era top marginal income tax rates, and Democrats got an extension of unemployment benefits, plus the repeal of "Don't ask, don't tell." It should have been a win all around, but after Obama got the lion's share of the credit, House Republicans soured on the deal.

Where Republicans are going wrong now is that they haven't put anything on the table to demonstrate that what they want is a deal and not a contest to see who will blink first.

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There's been no offer to move immigration reform, no offer to let Obama's judicial nominations pass and no recent talk of a longer-term deal with tax and entitlement reform. And so far Republicans haven't even taken up the Senate's offer of a short-term budget resolution with the lower government-funding levels that kicked in earlier this year.

If the GOP wanted "chained CPI," a flatter income tax structure or something else on their wish list, they could trade for it. But considering the history, congressional Republicans haven't given the president that much incentive to counteroffer.

And while it's fair game, of course, to oppose Obama's policies β€” after all, that's the opposition's job β€” they've made a pretty weak case when they say he won't compromise.

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The president has consistently run a middle course.

For now, Republicans won't take yes for an answer.

David Swerdlick is a contributing editor at The Root. Follow him on Twitter.

David Swerdlick is an associate editor atΒ The Root.Β Follow him on Twitter.Β