E. W. Jackson, Jamie Radtke, Del. Robert G. Marshall and George Allen participate in their third and final Republican primary debate for U.S. Senate in Virginia. (Richard A. Lipski/FOR THE WASHINGTON POST)

George Allen has a Republican primary to win if he hopes to face fellow former governor Timothy M. Kaine (D) this November in the race for a Senate seat from Virginia.

But you would hardly have known that as Allen joined Gov. Robert F. McDonnell (R) for a Monday rally that was much more focused on the general election than Tuesday’s balloting.

The Republican Senate nod is the biggest trophy up for grabs in Virginia as voters go to the polls Tuesday to select nominees for congressional seats and a few local offices.

Polls will be open across the state from 6 a.m. to 7 p.m. Because Virginia does not register voters by party, any voter may choose to cast a ballot in the Republican primary, but turnout is expected to be low. The state’s new law requiring voters to show identification before their ballots will be counted does not take effect until July 1, so it will not apply to Tuesday’s primary.

Allen is the front-runner in a Republican field that also includes Chesapeake minister E.W. Jackson, Del. Robert G. Marshall (Prince William) and former Virginia Tea Party Patriots head Jamie Radtke. A Washington Post poll released last month found Allen leading the primary contest with 62 percent of the vote.

The same survey showed Allen and Kaine tied in the prospective general election matchup to succeed retiring Sen. James Webb (D). Several other surveys also have shown them to be neck and neck.

“Majority control of the U.S. Senate could be determined right here in Virginia with George Allen,” McDonnell said at Monday’s rally, held at the Ashburn headquarters of Prototype Productions, a defense and technology manufacturing firm.

Allen asked attendees to vote Tuesday to “send a message to President Obama, Tim Kaine and their Washington allies.” He made no mention of his Republican opponents, keeping with his practice throughout the primary campaign.

Radtke, meanwhile, has been airing a late round of radio and television ads, and she said Monday that “conservatives and tea party supporters across Virginia see the opportunity tomorrow to topple the establishment-picked, career politician George Allen and send a new generation of leadership to Washington.”

Jackson made stops in Chesapeake and Virginia Beach and did media interviews Monday. Marshall’s campaign did not respond to a request for comment.

All three Republican underdogs have sought to attack Allen from the right, arguing that he is insufficiently conservative — particularly in his voting record in his previous term in the Senate — to deserve the nomination.

Farther down the ballot, retired Army Col. Chris Perkins and traffic engineer Ken Vaughn are fighting for the Republican nomination to face Rep. Gerald E. Connolly (D) in the Fairfax-based 11th Congressional District.

The winner of the GOP nod will be considered the underdog against Connolly, who has a $1 million campaign war chest. Connolly held the seat by fewer than 1,000 votes against Republican Keith Fimian in 2010, but the district has since been redrawn to be more favorable to Democrats.

Rep. James P. Moran Jr. faces a challenge in the Democratic primary from Navy veteran and business consultant Bruce Shuttleworth, but the incumbent is strongly favored to prevail in the district that includes Alexandria, Arlington, Falls Church and a portion of Fairfax County. Shuttleworth has sought to raise questions about Moran’s integrity, but Moran has defeated
better-known and better-funded challengers in the past.

Elsewhere in the state, Reps. Eric Cantor, Randy Forbes and Bob Goodlatte are expected to survive Republican primary challenges.

In Alexandria, Democrats will choose six nominees for the City Council from among 14 candidates.