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The state had a more moderate December jobless rate of 6.4 percent and has a potent labor movement, with 22 percent union membership, one of the nation's highest rates.
Alaska has a state minimum wage of $7.75, which exceeds the federal level and is expected to rise further with a ballot initiative this summer increasing the state minimum to $9.75 in 2016.
And though Obama is as unpopular in Alaska as in Arkansas, Alaska has many independent voters and an entrenched working-class ethos.
"I listened to a whole lot of diatribes against Obama," said Ed Flanagan, a former state labor commissioner who said he gathered signatures for the minimum wage ballot initiative in conservative areas. "But they signed the petition."
Begich seems unconcerned about backing Obama on the minimum wage.
"I've got plenty to separate myself from the president" on higher-profile issues, Begich said, citing differences over federal curbs on energy development and his opposition to expanding gun buyers' background checks.
Other senators facing voters this year who must also gauge home-state sentiment include Democratic Sen. Mary Landrieu, who must be careful to not tie herself too closely to Obama in conservative Louisiana. She said she supports an increase, but $10.10 would be "a pretty significant jump" for Louisiana, which has no minimum of its own.
Sen. Susan Collins, R-Maine, said she worries about the size of the $10.10 proposal. She said she was working with other Republicans on an alternative with incentives to keep small businesses from cutting jobs.
The $10.10 proposal got mixed reviews last week from the nonpartisan Congressional Budget Office. It said the increase could cost the economy 500,000 jobs in 2016, while lifting 900,000 people over the poverty line.
That hasn't deterred Democrats from seeking Senate votes.
"Bring it up. And when you don't get 60 votes, bring it up again," said Brad Woodhouse, president of the liberal Americans United for Change. "It's one of those things where the politics are so good for Democrats."
"Democrats are trying to refocus the national conversation around anything but the two major issues that have plagued them for the last several years" — Obama's 2010 health care overhaul and the economy, said Brad Dayspring, spokesman for the National Republican Senatorial Committee, the party's Senate campaign arm.