(CNN) They're making their case in Washington, in the early states and even on foreign trips: The governors vying for the presidency in 2016 say that their party must nominate a candidate who has led a state.

But for a handful of Republican governors eyeing the White House, their popularity at home is taking a hit.

Poll numbers for New Jersey Gov. Chris Christie and Louisiana Gov. Bobby Jindal have reached rock bottom as their states confront fiscal woes; the problems are particularly severe for Christie, whose reputation in the Garden State has been badly damaged by the so-called Bridgegate political scandal. And Gov. Scott Walker of Wisconsin has seen his approval rating in his home state fall amid a divisive budget battle, even as his star has risen in national surveys.

Their declining home-base standings illustrates a unique predicament that sitting governors face when exploring a presidential campaign.

Governors have to juggle maintaining a close bond with the voters who elected them while wooing supporters in far-away primary states. A governor's absence is conspicuous to local press and constituents in a way that U.S. senators' travels outside of their states are not. And while senators are scrutinized for years' worth of votes, governors have the challenge of defending the performance of an entire state.

It's not just current governors who are scrutinized for their in-state records. Former Maryland Gov. Martin O'Malley, who is widely expected to seek the Democratic Party's nomination for president, has come under fire from critics in the aftermath of the riots in Baltimore for his law enforcement policies

Former Republican Utah Gov. Mike Leavitt said sitting governors with presidential ambitions have faced special obstacles for years. He recalled former Massachusetts Gov. Michael Dukakis, who ran for president in 1988, telling him that he couldn't have managed being a White House candidate were New Hampshire -- where one of the most important primary contests is held -- not a neighboring state.

Balancing governing at home with campaigning

"There's a constant tension between present obligation and future ambition," Leavitt said in an interview. "There's a requirement that the governor have their affairs in order at home in order to concentrate on any future endeavor -- like running for president."

The problems seem especially acute this time for the governors considering fighting for the GOP nomination for president.

Christie's approval sunk to its lowest level yet last month: 56% of voters disapprove of his performance as governor while 38% approve, according to a Quinnipiac University poll . Another troubling sign is that seven in 10 of Christie's New Jersey constituents believe the governor is "more concerned about his own political future" than governing the state, a Monmouth University survey earlier this month found.

A Jindal's numbers have also reached new lows. Southern Media & Opinion Research survey this week showed the governor with an "all time low" 32% positive job performance rating. This follows a Triumph Campaigns poll in March that had his approval rating at 27%.

Walker's approval in Wisconsin also has dropped, falling to 41% in April from 49% in October, according to a Marquette Law School poll

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Prominent party leaders in New Jersey and Louisiana are publicly grumbling.

Louisiana Lt. Gov. Jay Dardenne said in an interview that there is a "significant level of frustration" in his state about Jindal's absence, particularly as the Legislature grapples with getting its fiscal house in order.

"The governor is spending his time in Iowa and New Hampshire and South Carolina. ... The public is starting to take notice of his focus on his future rather that the state's future," said Dardenne, who is campaigning for governor (Jindal is term limited from running again). "He has basically abdicated that responsibility to the Legislature, and the Legislature, as it should be, is grappling with what to do and it's a tough situation."

For Christie, "Bridgegate" alone seems to have "stopped his momentum cold," said former New Jersey Gov. Tom Kean Sr., a Republican who has supported Christie in the past. While Kean said he wouldn't blame Christie for all of New Jersey's fiscal problems, he noted the governor has "had a while to fix it now and he hasn't."

Kean cautioned that parts of Christie's record in New Jersey will be a liability for the governor on the national stage: When "reporters come into the state to evaluate Gov. Christie's record and find a lot of unsolved problems, that's a real negative because he's running on: 'I can do for the country what I can do for New Jersey.'"

For Christie, Jindal and Walker, painful home-state budgeting have been central to their problems.

Bleak fiscal outlook in New Jersey

In the Garden State, where Christie won re-election in 2013 by a wide margin, the fiscal outlook is bleak.

Moody's announced yet another downgrade of the state's debt last month, putting in sharp focus the dismal state of New Jersey's long-troubled finances, which have been roiled by a revenue shortfall and massive pension obligations. Only one other state -- Illinois -- had a lower rating than New Jersey at the time of the downgrade, and a negative outlook signals that analysts do not expect things to get better any time soon.

"If they have not made meaningful improvements to their budget and pension obligations, the state's rating will continue to fall," said Baye Larsen, a Moody's analyst who emphasized how politically difficult it is to adopt sweeping pension reforms.

Louisiana also faces a host of economic issues.

The Southern state was badly damaged by Hurricane Katrina 10 years ago. Reconstruction efforts following the devastation have given the state's economy a boost, but progress has started leveling off. Most recently, Louisiana's revenue stream has taken a hit from low gas prices, while reliance on what analysts refer to as "one-shot" budgeting solutions and a high pension liability have also taken a collective toll.

"It has been kind of a perfect storm," said Marcia Van Wagner, an analyst with Moody's, which in February revised the state's outlook to "negative."

In Wisconsin, Walker has a tough task of selling a deeply controversial budget proposal that's been met with fierce opposition. The governor rose to national fame as a union-busting fighter who fended off a historic recall effort. Now, some of the sweeping cuts Walker has proposed, including to the University of Wisconsin system, are deeply unpopular in the state.

"This is not a very popular budget right now, the way that it was presented by the governor in February," said state Senate Majority Leader Scott Fitzgerald, a fellow Republican. But Fitzgerald said Walker has been fully engaged with members of the Legislature even as he's traveled out of Wisconsin to court donors and visit early states, and he dismissed the governor's recent decline in the polls as temporary.

Christie, meanwhile, faces political dilemmas that extend beyond New Jersey's fiscal health.

The political scandal dubbed "Bridgegate," which took place in September 2013, remains a dark cloud hanging over the governor and his political ambitions. In early May, two senior officials with ties to Christie were indicted in the infamous lane closures on the George Washington Bridge, while another pleaded guilty to conspiracy to commit fraud and conspiracy against civil rights. U.S. Attorney Paul Fishman said other alleged co-conspirators may be named at a future date.

As the 2016 Republican field begins to take shape, it's unclear how much the governors' in-state challenges will affect their national standings.

Scott Walker's numbers improve

Walker has seen his national stock soar nationally. In an April CNN/ORC poll , the Wisconsin governor trailed just former Florida Gov. Jeb Bush among likely 2016 GOP candidates, getting 12% of the support among Republicans and Republican-leaning independents -- up significantly from 4% in December.

Christie's national backing has taken a hit, falling from 13% in December to 4% in April. Jindal tracked in the low single digits in the CNN/ORC poll, with just 2% of support among Republican and Republican-leaning independents in the survey.

A Jindal spokesperson did not respond to requests for a response, and spokespeople for Christie and Walker referred CNN to the governors' recent public comments about their popularity at home.

"These things are all temporary snapshots of time and nothing that concerns me much at all," Christie told reporters in April. "I've been up in polls, down in polls."

Walker said on Fox News last week that it's "pretty common" for Wisconsin governors to see their approval rating dip every two years and noted that he won the recall election in 2012 by a bigger margin than when he was first elected governor in 2010.

Matt Strawn, former chairman of the Iowa Republican Party, said he doesn't believe Iowa caucusgoers are preoccupied by local approval ratings.

"That personal retail nature of Iowa caucus very may well be an antidote to whatever polling a potential candidate may have back home," Strawn said. "The fact that especially Gov. Christie and Gov. Walker were able to win multiple elections in states not traditionally hospitable to Republicans says more than any temporary snapshot of approval ratings back home."

But others think the governors' state records could ultimately hurt them.

"They are running on what they've done in the state," Kean said. "So if a state starts turning around on him or things don't go well in the state, that's going to be a reflection because they haven't done much else except be governor."