Several states and the District of Columbia are going to the polls for state primaries on Tuesday. Will Tea Partiers upset establishment picks in Delaware and New Hampshire? Will Mayor Adrian Fenty lose in Washington D.C.? The Daily Beast on what to watch.

Delaware

Much of what would help Rep. Mike Castle win Joe Biden’s old Senate seat in a general election is what’s sinking him in the Republican primary: He’s an establishment politician who’s held elected office in Delaware for the past 30 years as a pro-choice, pro-gay moderate—a RINO, or Republican In Name Only, according to some conservatives. His Tea Party-backed opponent, Christine O’Donnell, is gaining on him, pulling ahead of Castle in the latest Public Policy Polling survey. O’Donnell also earned the endorsement of Sarah Palin, who recorded robocalls on her behalf. O’Donnell has a long list of past financial problems, including an IRS lien and a near-foreclosure, as well as a history of losing elections. If O’Donnell triumphs Tuesday night, the Republicans’ chance of winning Biden’s old seat—and of retaking the Senate—drops significantly.

New Hampshire

The frontrunner, and establishment pick, in New Hampshire’s Republican primary for the Senate seat of Judd Gregg is Attorney General Kelly Ayotte, who has even been dubbed a “mamma grizzly” by Sarah Palin this year. But the Tea Party favors Ovide Lamontagne, a businessman who has earned the endorsement of the Union Leader, the state’s influential newspaper. Another businessman, Bill Binnie, has dumped a ton of his own cash into the race, billing himself as a fiscal conservative with moderate social views. If Ayotte secures the nomination—and she’s still polling ahead by a few points—Republicans have a solid chance of keeping a seat they’ve held on to for three decades. But Lamontagne has the momentum, pulling within four points, even though he trails in polls against the Democratic nominee, Paul Hodes.

Washington, D.C.

• Benjy Sarlin: How the GOP Could Lose the Tea Party• John Avlon: The Tea Party's Northern Insurgency• Samuel P. Jacobs: Frontrunner FolliesMayor Adrian Fenty, a determined reformer who swept into office in a landslide in 2006, has quickly found himself an underdog in his bid for reelection. Up against D.C. Council Chairman Vincent Gray, the most recently available poll of the race puts Gray 17 points ahead among likely voters, with a large edge among the black voters that handed Fenty the mayor’s office in the first place. Though the incumbent mayor has delivered on many of the tough reforms he promised in his initial campaign, such as restructuring the public-school system, he has faced a backlash for not maintaining his ties to the community. Gray, now the frontrunner, has also attacked Fenty on ethics charges, claiming he has funneled millions in taxpayer money to his “frat brothers” and “cronies.”

New York

Longtime New York Republican pol Rick Lazio is struggling in the Republican gubernatorial primary against Carl Paladino, whom The Daily Beast’s John Avlon describes as a “Tea Party hypocrite”—the kind who preaches fiscal conservatism yet holds $85.3 million in state government contracts. Paladino “began his self-funded campaign with the exposure of a series of emails that manages to include racism (African tribal dances described as Obama inauguration festivities) and bestiality (sex with horses, if you must know) and somehow went down from there.” A Siena poll found Lazio up by a single point last week, even though as late as early July, Lazio was ahead by 20 points.

The once-proud New York Republican Party couldn’t find anyone with statewide credentials to run against Sen. Kristen Gillibrand, and so three little-known men are fighting it out in the primary. Forbes columnist and economist David Malpass is a fiscal wonk, Bruce Blakeman is a businessman, and Joe DioGuardi is an outsider—at least according to his own campaign. Despite years in elected office, and working as a registered lobbyist for Albania, DioGuardi has name recognition that’s rubbed off from his daughter, a former judge on American Idol. Gillibrand, appointed to replace Hillary Clinton, should have been easy to pick off in this difficult year for Democrats, but none of these candidates is expected to stand much of a chance against her.

Wisconsin

While Senator Russ Feingold, Wisconsin's sitting senator who was elected to the position in 1993, has no Democratic opponent, falling approval ratings have prompted him to go on a spending spree to assure that he hangs in there—he's already spent $11.4 million this election cycle. Meanwhile, on the GOP's side, plastics company owner Ron Johnson and small-business owner David Westlake are the top competitors on the Republican ballot. A Rasmussen poll from late August showed both Johnson and Westlake neck and neck with Feingold, with Johnson taking a slight lead. Johnson certainly has more money in his wallet to allocate to his campaign; Johnson is one the richest self-funded candidates of 2010.

The race for Wisconsin's 7th Congressional District seat is also heating up. On the GOP side, District Attorney Sean Duffy—yes, that guy from The Real World—has raised $1.2 million, a handsome sum that certainly dwarfs competitor Dan Mielke's $500,000. Mielke is a farmer and business who mounted an attack on Duffy for his support of civil unions.

Rhode Island

Tuesday is expected to be pretty quiet in the Ocean State. One race to keep an eye on: Providence Mayor David Cicilline is the best-funded and best-known candidate in the four-way Democratic primary for the seat being vacated by Patrick Kennedy. If he is elected, he will be just the fourth openly gay member of Congress.