Polls opened Tuesday for New Jersey's primary election where a former U.S. attorney and a former North Jersey mayor are competing in the Republican gubernatorial contest -- a critical seat the GOP is vying to capture from sitting Democratic Gov. Jon Corzine.

Chris Christie, widely seen as a moderate conservative, expressed confidence Tuesday in beating his Republican opponent, Steve Lonegan, who is running on a more conservative platform.

"It's been an engaging campaign," Christie told reporters after voting early Tuesday in Mendham Township, N.J.

Christie called Lonegan a "very formidable opponent," who has spent "a lot of money."

Republican Assemblyman Rick Merkt -- also a contender in the race -- lags behind both candidates in the polls.

Lonegan has dismissed polls showing him trailing Christie. Casting his vote in Bogota, N.J., on Tuesday, Lonegan said a poll taken a week and a half ago is not relevant to what is happening today. Lonegan has trailed Christie in most polls, but is counting on a surge of conservative votes to close the gap.

The GOP hopes to defeat Corzine, who has trailed considerably behind both Christie and Lonegan in polls in recent weeks.

A Research 2000/Daily Kos poll released Thursday shows Christie with a 7 percentage-point lead over Corzine -- 46 percent to 39 percent. Lonegan led the governor by 3 percentage points -- 43 percent to 40 percent -- according to the poll.

"I'm going to wake up every morning thinking about how to make government smaller and more efficient as governor and return tax money to the people," Christie told reporters Tuesday. "Governor Corzine wakes up every morning thinking about growing the government."

Vice President Joe Biden is expected to join Corzine to launch his re-election bid after the polls close at 8 p.m. ET.

Mayoral contested primaries are also being held in Camden, Atlantic City and Edison.

Meanwhile, the Democrats are in a tight three-way race for the governorship in Virginia -- another critical race that Republicans see as a must-win. Creigh Deeds leads his Democratic opponents by 27 percent, followed by Terry McAuliffe at 24 percent, and Brian Moran at 22 percent, according to a recent survey conducted by Public Policy Polling.

Sitting Democratic Gov. Tim Kaine is prevented from running for re-election because of term limits.

The winner of Virginia's Democratic gubernatorial primary will run against Bob McDonnell, the state's former attorney general and Republican nominee who now leads all three Democratic contenders in the polls.

Virginia has long held a strong Republican base, but the state went for President Obama in the 2008 presidential election.

FOX News' Sarah Courtney and the Associated Press contributed to this report.