The old adage says all politics are local. But challengers this year are convinced that national dissatisfaction with Iraq, immigration and political corruption give them an unusual chance to topple sitting governors, senators and House members.

Primaries on Tuesday for governor in Alabama and California, a Senate seat in Montana and a handful of House contests, among other races, will put their faith to the test.

The most-watched congressional contest is the only one that will actually put someone in office — a special election in southern California to replace jailed former Rep. Randy "Duke" Cunningham. Democrats hope to win in what has long been a conservative, GOP stronghold, and the race is seen as a bellwether for fall midterm elections.

In all, eight states are holding primaries, with polls also open in Mississippi, New Jersey, New Mexico, South Dakota and Iowa, where there is an open governor's seat.

In Montana, revelations of three-term Republican Sen. Conrad Burns' ties to convicted lobbyist Jack Abramoff have made him one of the most vulnerable members of Congress, inspiring a vigorous contest among Democrats for the right to face him this November.

The issues in Alabama include tax policy, social conservatism and immigration, as GOP Gov. Bob Riley's failed tax increases have spurred both a Republican primary and a heated contest among Democrats. Former Judge Roy Moore is challenging Riley for the GOP nomination, after gaining social conservatives' notice for his unsuccessful fight to put a Ten Commandments monument in his courthouse.

Among the Democrats hoping to get Riley's job is former Gov. Don Siegelman, who will likely be in federal court on racketeering and bribery charges. His toughest opponent is Democratic Lt. Gov. Lucy Baxley.

In California, early polls that showed a drop in GOP Gov. Arnold Schwarzenegger's popularity raised Democratic hopes. But he's benefited from a mean-spirited Democratic primary campaign between Treasurer Phil Angelides and Controller Steve Westly. Schwarzenegger faced no major primary competition.

"It seems clearly to be a time when people are not real happy and not thrilled with incumbents almost anywhere," said Norm Ornstein, a political analyst at the American Enterprise Institute. "There's no doubt you're getting highly attractive (challengers) running because of the peculiar circumstances."

It's always uncertain whether national dismay will trickle down when people vote for their own members of Congress, and the connection is even harder to make to governors.

But already this year, possible signs of anti-incumbent sentiment have emerged in Oregon, where Democratic Gov. Ted Kulongoski won a hard-fought primary with only 54 percent support; GOP Rep. Don Sherwood, a Pennsylvania congressman, faced a surprisingly strong challenge from a poorly funded, little-known opponent; and voters threw out more than a dozen Pennsylvania state legislators over a legislative pay raise.

Polls track the discontent: An AP-Ipsos poll last month found the electorate's mood souring, with 73 percent of those polled saying the nation is on the wrong track. That poll had President Bush's approval ratings down to a low of 33 percent, with Congress even lower at 25 percent.

The efforts to highlight discontent over national issues pops up in primary campaigns everywhere. Immigration has been argued in Alabama, California and New Mexico; Iraq in California and New Mexico; political corruption in Montana; ties to oil companies and complaints about gas prices in California; abortion in Iowa.

California's special election pits Republican former House Rep. Brian Bilbray against Democrat Francine Busby for Cunningham's former seat in a conservative San Diego-area district. It's brought national money and speculation that a Democratic win would be a taste of bigger victories in the fall.

Their ads: Bilbray featured his fight against illegal immigration, while Busby promised higher ethical standards.

Democrats also are hoping for a critical autumn victory in Montana, where Burns, seeking a fourth term, has denied that Abramoff or his money ever influenced him. He has blamed the "Eastern liberal press" for his troubles and predicted that Montana voters "will make the right judgment call."

Among other races that Tuesday's primaries will sort out for the fall:

— An open governor's seat in Iowa brought out four Democrats hoping to face GOP Rep. Jim Nussle.

— Republican Tom Kean Jr., son of the former governor, was favored in the GOP primary to challenge New Jersey Democratic Sen. Robert Menendez.

— Former California governor and presidential candidate Jerry Brown, term-limited from staying on as Oakland mayor, is running for state attorney general.

In many cases, Democrats are hoping to capitalize on anti-incumbency sentiment — a reflection on the GOP control of the House, the Senate and a majority of the nation's governorships.

"All the short-term factors are working in the Democrats' favor," said Merle Black, an expert at presidential and Southern politics at Emory University. "To the extent that these elections are nationalized, the Democrats ought to come out better. But I don't know if the national thing really plays out in state contests."