When Mitt Romney and George Allen campaign together this Saturday, it will be the first time the Republicans have managed to do so in Virginia this year. Timothy M. Kaine says his support for Barack Obama is unwavering, but the former governor is careful to point out differences he’s had with the president, whether on taxes, Libya or offshore drilling.

Virginia’s U.S. Senate contenders aren’t exactly running away from their parties’ presidential candidates, but they are leaving enough wiggle room to appeal to two slim but vitally important slices of the electorate: Romney-Kaine and Obama-Allen voters.

Their numbers are barely enough to rise above the margin of error in political polls, but Virginia’s ticket-splitters are more than sufficient to make the difference in two very tight races. These are voters for whom President Obama and former governor and senator Allen, despite the ideological gulf between them, seem like the candidates of change, men who understand regular folks and can break through the political paralysis.

Conversely, the other set of splitters sees Romney, who will take a bus tour through the state on Saturday, and Kaine as the adults on the ballot — serious, effective leaders with the capacity to rise above partisan differences.

In the complex interplay between the presidential and Senate campaigns in one of the nation’s most crucial swing states, the hunt for a relative handful of ticket-splitters takes place in a quieter corner, far from the war zone of more than $100 million in ads aimed at Virginia voters.

In phone banks, retail politicking and conversations with donors, the Allen and Kaine campaigns are scurrying to identify and court Virginians who may well go a different direction for Senate than they do for president.

“People for whatever reason do like President Obama, and they do think things need to be changed,” Allen said as he campaigned at a rodeo show at the Loudoun County Fair. He cited support for veterans and funding for higher education as areas where his appeal and Obama’s overlap.

Allen’s wife, Susan, who has appeared with Romney, said she can understand why some voters are drawn to both the president and her husband.

“I’ve run into people who said they’re going to vote for Obama and they really like George. They trust him, and they know him,” she said.

In a Washington Post poll in May, 5 percent of Virginia voters said they were voting for Romney and Kaine and 7 percent supported Obama and Allen.

Some Kaine advisers scoffed at those figures, saying that finding real Obama-Allen voters would be nearly impossible.

But they’re out there. Roger Quiroz, 24, is a banker in Fairfax who has voted for Obama and Kaine. He said he’s leaning toward Obama this year “because things were in a rut when he came in and it’s not fair to hold that against him. . . . Romney has that business background, but he’s so much for the rich.”

For the Senate seat, however, Quiroz is ready to mix it up. “I haven’t seen much change in Virginia, and it’s not totally Kaine’s fault, but I just want better results,” he said. “In my job, I see foreclosures, people upset about their interest rates, people getting their cars repossessed.”

What Obama and Allen have in common, in Quiroz’s thinking, is an orientation toward change.

“In a close race, that small cell of Obama-Allen voters could be the determining factor,” said a senior Allen strategist, who insisted on anonymity because he was not authorized to speak for the campaign. “These are people who were very supportive of the president last time, and they still like him personally and want him to succeed. Their anger is more directed at Washington than at the president. These are people we’re going after, helping them see George Allen as someone who’s going to change what’s going on in Washington.”

Melissa Kelly shares Quiroz’s worry about the economy but ends up in a very different place. After two years of looking for work, she has found nothing in the fields in which she has degrees — criminal justice and business management. She’s working part-time at a cafe in a pharmacy in Chesapeake.

Although nominally a Democrat, she voted for John McCain in 2008 and is lining up with Romney and Kaine this fall.

They’re both straight shooters, she said, and seem devoted to fiscal reform without unduly bashing the government (her fiance has a federal job). She parts with Romney on taxing the rich, but she believes he’d focus more on jobs and the economy than Obama. Kaine, Kelly said, “is open, honest, straightforward. He tells it like it is.”

In an interview, Kaine said he hasn’t found many living, breathing examples of the Obama-Allen voter. But he said he sees plenty of evidence of the opposite phenomenon; his donors include “a lot of Romney folks,” some of whom “didn’t like things George did.”

On the surface, the presidential and Senate campaigns say they’re in sync.

“President Obama and Governor Kaine have a long relationship, and they support each other fully,” said Frank Benenati, spokesman for the Obama campaign, who added that “we do expect that they will campaign together in the future.”

The Obama camp expects to help Kaine with blacks, immigrants and seniors, and calculates that Kaine will bring the president votes in the white working class and among veterans.

Republicans in the Romney and Allen campaigns, as well as Virginia Victory, the state party’s coordinated campaign, say their strategy of relentlessly linking Kaine to Obama will work. “Pairing Obama as tax-raiser-in-chief and Kaine as his top attack dog in Washington is a very good thing,” said Pete Snyder, chairman of Victory.

But behind the scenes, some top Republicans worry that the same factors that led to Allen’s loss to Sen. James Webb in 2006 — a growing number of socially liberal voters in Northern Virginia, increased ethnic diversity statewide, and Allen’s history of brash talk — could leave him lagging behind Romney.

In 2008, “tens of thousands of Virginia voters voted for a Democrat for perhaps the first time in their lives,” said a senior Virginia Republican strategist. “And some of them thought George Allen was an abomination in 2006, with the macaca thing and all that, and just can’t go there. Those are your Romney-Kaine voters.”

Active presidential campaigns have not been the norm in Virginia. That changed in 2008, when Obama capitalized on demographic change that brought hundreds of thousands of new voters to the state, many of them young, non-white, immigrant or highly educated families.

Many of those new voters tend to vote more for personalities than for party, strategists from both parties said, pointing to Sen. Mark R. Warner (D) and Gov. Robert F. McDonnell (R) as examples of Virginians choosing candidates who seem able to get things done.

That has the Kaine camp hopeful they can win even if Obama loses Virginia. “I’m seeing Republican business people, especially in Northern Virginia, say, ‘We’re not crazy about Mitt Romney, but he’s better than Obama, and George Allen is certainly not our kind of Republican,’ ” a senior Kaine strategist said.

Kaine is walking a fine line between fighting back at Allen’s efforts to portray him as Obama’s sidekick and embracing that image because of the president’s popularity among some groups.

“This is the one swing state other than Ohio where the Democratic Senate candidate is not being bashful in his support for the president,” the Kaine strategist said. “But he will distinguish himself where he needs to.”

Allen said his campaign will continue to hammer away at Kaine, portraying him as a carbon copy of Obama, even if Kaine does point out their differences.

“People won’t be fooled by that,” said Allen, some of whose ads end with this tag­line: “Tim Kaine. President Obama’s Senator. Not Virginia’s.”