The Republican Party is already at war with itself, but its fight is spreading. This time it's not conservatives versus moderates. The new feud, exacerbated by the government shutdown, is between Republicans inside the Beltway and those on the outside.

For congressional Republicans, the high-stakes spending fight that closed the government was supposed to reaffirm the GOP's commitment to conservative principles, fire up their base and lay the foundation for a political payoff in the 2014 elections and beyond.

But among Republican governors, there's a fear that the showdown will bring the party plenty of trouble in future elections.

Led by Louisiana Gov. Bobby Jindal, the governors launched a media blitz they say is needed to limit the damage "dysfunctional" Republicans in Washington are inflicting on the GOP brand and to show voters that -- on the state level, at least -- Republican leaders are translating conservative principles into policies that resolve the problems of real people.

"We've got 30 Republican governors," Jindal, the head of the Republicans Governors Association, said on MSNBC's "Morning Joe" program. "We said we're going to to stop outsourcing our brand to Washington, D.C., because if you want to see conservative ideas being applied, it's not happening in D.C. It's happening in our state capitals."

Jindal is being joined by current and former Republican governors -- some of whom are expected to make presidential runs in 2016 -- who see the chaos in Washington as an opportunity for them to rise above the fray. Wisconsin Gov. Scott Walker, New Jersey Gov. Chris Christie and former Florida Gov. Jeb Bush have each scoffed at the antics of congressional lawmakers, even those within their party.

Some Republicans in Congress were initially reluctant to get into a budget fight that could lead to a government shutdown, but all have sustained the battle hoping it will ultimately payoff in next year's election. So far, that isn't how it's working out.

Just 24 percent of voters approve of the way Republicans are handling the budget negotiations, A Washington Post/ABC News poll showed. That puts the GOP behind both President Obama (45 percent approval) and congressional Democrats (35 percent).

But House Republicans in particular are playing to a skewed audience: Constituents in their safe Republican congressional districts are urging them to continue the fight.

Many Republican governors have been compelled by political realities to moderate their politics, including Christie and Walker, both of whom were elected in Democrat-leaning states. While Washington Republicans equate compromise with failure, the two governors openly trumpet their bipartisan credentials.

“I think everybody has handled it poorly,” Christie said of the congressional budget impasse. He subsequently ran a campaign ad that alerted voters to his bipartisan credentials.

“I think as long as you stick to your principles, 'compromise' isn’t a dirty word,” Christie said in the ad.

"Blame can go around for everybody," Walker told the Associated Press. "The best way to resolve it? Just look at what we did in Wisconsin. We had a $3.6 billion budget deficit. We now have more than half a billion surplus."

The divide between Republican factions inside and outside the Beltway could reemerge in the 2016 presidential primaries — and that's no coincidence. Christie, Bush, Walker and Jindal are all rumored to be weighing bids for their party’s presidential nomination, and some of their most serious competitors are on the front lines of the ongoing congressional battle.

Sens. Marco Rubio, R-Fla., Ted Cruz, R-Texas, and Rand Paul, R-Ky., all considered top potential presidential contenders, have been at the forefront of the fight over government spending and GOP attempts to weaken or derail Obamacare. Cruz, in particular, has emerged as a leader of the movement and staked much of his reputation on the debate's outcome.

Meanwhile, Republican governors have had the luxury of weighing in on the government shutdown from afar — and without being forced to vote on it.

And to the GOP governors’ advantage, even some Republicans in Congress tend to agree with the outsiders' harsh assessments.

“I agree, we do need to get our act together,” said Rep. John Fleming, R-La. “The problem is, it’s like a dysfunctional marriage. You’ve got to have both sides who go to the counselor to get something together on that.”