A key part of the GOP's strategy on the sequester is to blame President Obama for the fact it exists at all. One good example is House Speaker John Boehner's op-ed in today's Wall Street Journal:
With the debt limit set to be hit in a matter of hours, Republicans and Democrats in Congress reluctantly accepted the president's demand for the sequester, and a revised version of the Budget Control Act was passed on a bipartisan basis.
Ultimately, the super committee failed to find an agreement, despite Republicans offering a balanced mix of spending cuts and new revenue through tax reform. As a result, the president's sequester is now imminent.
The big problem with this narrative is that it directly contradicts Boehner's rhetoric at the time. After the deal was crafted, in July 2011, Boehner told GOP House members that "There was nothing in this framework that violates our principles." Later, in an interview with CBS News following the House vote on the bill, he described the deal as such: "When you look at this final agreement that we came to with the White House, I got 98 percent of what I wanted. I'm pretty happy." And, as a whole, the House GOP was fine with the deal too—it passed 269-161, with 174 Republicans voting in favor.
It's possible that Boehner opposed the sequester, even as he praised the deal. But judging from his rhetoric, there's little sign that was the case.
Beyond Boehner's clear enthusiasm for the original debt deal, there's the simple fact that the sequester would have never happened if not for GOP intransigence. With the debt ceiling crisis, Republicans had taken the economy hostage, threatening a default if Obama didn't agree to immediate, massive spending cuts. After the GOP refused to pass a clean extension of the debt ceiling—and affirmed their willingness to pull the trigger—the White House crafted the sequester as a compromise measure, which—again—Republicans accepted as part of an overall deal.
Posturing aside, the GOP is not in a good position with the sequester. The public supports Obama's push for a "balanced" approach of revenue and spending cuts, and is broadly dissatisfied with the GOP's approach to governing. This narrative on the sequester might play will with Republican voters, but it does little to convince more moderate Americans, who just don't trust that the GOP is acting in good faith.