(AP Photo/J. Scott Applewhite) (AP Photo/J. Scott Applewhite)

Usually in the aftermath of a major political battle, both sides argue that they have emerged victorious.

But as the federal government reopened Thursday, Republicans did something unusual: they trumpeted how badly they had lost.

“We fought the good fight. We just didn’t win,” House Speaker John Boehner (R-Ohio) told a Cincinnati radio host in his only public comments Wednesday.

To some extent, this was acknowledging the obvious, since the budget deal was forged on President Obama's terms, with virtually no concessions to the GOP.

But it also shows how Republicans across the ideological spectrum can share the same sentiment -- that they lost -- while drawing very different conclusions.

For Sen. John McCain (R-Ariz.), who told CNN's "New Day" that Obama won the standoff, this means lawmakers will be compelled to reach a more lasting agreement to avert another shutdown. He predicted that the Senate and House will reach a budget deal hopefully “for a year,” but not without a “fight” within the GOP.

For conservatives such as Rep. Mick Mulvaney (R-S.C.), who helped lead the shutdown effort in the House, it means they need to push harder to restrain government spending beyond what was enshrined in the temporary continuing resolution. “I don’t know how you look at it as a victory,” Mulvaney said in an interview with the Fort Mills Times. “I don’t see that as a success.”

And for the Minnesota GOP, it's an opportunity to mobilize the base. The party sent out an e-mail with the tagline, "In a Broken Washington, Democrats Prevail."  The e-mail said that the "ugly deal" shows why Democrats shouldn't be trusted to run the government.

Taking direct aim at Sen. Al Franken (D-Minn.), the e-mail asked, "And where was Al Franken?  Laying low until after the deal was done; and then taking credit for such a glorious outcome for America."

"It is time for new leadership in Washington D.C.!" it exclaims, in bold.

The fact that Republicans are admitting defeat, in other words, is actually just another battle cry. And as the 2014 elections draw closer, this new compromise could push the GOP further away from, rather than closer to, the center.