Washington (CNN) -- Voters in California accustomed to casting ballots in party primaries will see something very different on Tuesday: All candidates, regardless of affiliation, will compete in the same preliminary contest, with the top two finishers moving on to compete in the general election.
California is one of five states holding primaries Tuesday. Others include an intra-party fight in New Jersey that pits President Barack Obama against former President Bill Clinton and a fight for the U.S. Senate seat in New Mexico vacated by retiring Sen. Jeff Bingaman. Residents of two other states -- Montana and South Dakota -- will also vote Tuesday.
California's so-called "top two primary" is intended to stem political gridlock caused by elected officials at their parties' extremes. Similar measures are in place in Louisiana and Washington, but as the country's most populous state, California's ballot shakeup could mean big changes to state and national politics.
Voters in the Golden State approved "top two" primaries in a ballot initiative in 2010, a year after the state's legislature passed a measure instituting the new practice. In a bargaining move designed to break gridlock in the legislature, then-Gov. Arnold Schwarzenegger backed the nonpartisan primary measure, joining an effort that also included Willie Brown, the Democratic former mayor of San Francisco.
Eric McGhee, a policy fellow at the Public Policy Institute of California, said in the past similar reforms have not had a major impact on the political discourse.
"If you look at the impact that these reforms have had in other states, they haven't been very large," McGhee said. "California is about the only state where something of this kind has elected more moderates in the past."
California held "blanket primaries" in 1998 and 2000, in which all registered voters could cast ballots, regardless of party affiliation. The United States Supreme Court struck down the practice, saying it violated political parties' First Amendment right of association.
McGhee said California's previous history with open primaries leads him to believe "a few more moderates" will be elected in California this time around.
There are two Congressional races in California in which incumbents will be pitted against each other Tuesday, though the state's new system would make it possible for all to advance to November's general election.
Redistricting following the 2010 Census led to a matchup between Democratic Reps. Janice Hahn and Laura Richardson in the state's 44th Congressional District outside of Los Angeles. In the San Fernando Valley, Reps. Brad Sherman and Howard Berman are facing off in the 30th Congressional District.
Sherman and Berman are each long-serving members of the House -- Sherman has been in office for eight terms, while Berman is completing his 15th term on Capitol Hill. Both were re-elected in 2010 with large majorities, and both serve on the House Foreign Affairs Committee.
Given each man's longevity in office, it's considered likely that they will both garner enough votes in Tuesday's primary to move on to the general election. But in both the Berman-Sherman race and the Hahn-Richardson race, McGhee said it wasn't clear how the new "top two" primary would impact the bitter partisanship the measure was meant to combat.
"In neither one of the races is it entirely clear which candidate is more moderate and which one is more liberal," McGhee said.
In New Jersey, a political fight between two incumbent Democrats is turning into a battle of the surrogates: former President Bill Clinton has endorsed Rep. Bill Pascrell, while President Barack Obama has shown tacit support for Rep. Steve Rothman.
Rothman and Pascrell are both eight-term congressmen who won re-election in 2010 with more than 60% of the vote. The two men are fighting for the same northern New Jersey seat this year after redrawn congressional lines placed Rothman's hometown into a conservative district. Instead of challenging Republican Rep. Scott Garrett, Rothman moved to Englewood, where he once served as mayor, to run against Pascrell.
Obama, whom Rothman backed in 2008, met with the candidate at the White House on Friday. Photos showed the two politicians walking along the White House colonnade, though their meeting was private.
In a press release, Rothman's campaign said Obama "affirmed his support" for the candidate at the get-together, characterizing the move as a show of appreciation for Rothman's backing in 2008.
"President Obama asked me to come to the Oval Office today so that everyone will know that he supports me and wants me to help him with his agenda in his second term, as I have in his first," Rothman wrote in a statement.
But Josh Earnest, the White House deputy press secretary, was careful Friday not to label the meeting as a show of endorsement.
"It means that the president has a longstanding relationship with Congressman Rothman, is appreciative of the solid working relationship that they've enjoyed while the president has been in office. It's indicative of the priorities that they share," Earnest told reporters aboard Air Force One.
Earnest noted the president had not weighed in on Democratic primary contests between two incumbent members of Congress.
Pascrell, a Hillary Clinton supporter in 2008, appeared alongside Bill Clinton at a campaign rally in Paterson on Friday. Clinton told supporters he was offering his endorsement because of his success working with Pascrell in the past, including during his time as president.
Both Pascrell and Rothman were elected in 1996, the same year Clinton was elected to a second term in the White House. The two men have similar, reasonably left-of-center voting records in Congress -- in the campaign, Rothman has attempted to paint himself as the more progressive candidate, while Pascrell stumps as a pragmatic moderate.
No independent polling has been released in the New Jersey race.
In a Democratic U.S. Senate primary Tuesday, voters in New Mexico will choose between Rep. Martin Heinrich and the state's Auditor Hector Balderas. The two are competing to fill the seat currently occupied by Sen. Jeff Bingaman, a Democrat who announced in February he wouldn't run for another term.
The battle between Heinrich and Balderas has largely been devoid of any major policy disagreements or personal attacks, and in a debate Sunday, the two candidates largely went after the presumptive Republican candidate, former U.S. Rep. Heather Wilson.
The Albuquerque Journal reported the only major disagreement during the debate centered on corporate tax rates, with Heinrich saying he supported lower tax rates on companies in order to lure them to do business in New Mexico.
"I think we need to have a lower, flatter, across-the-board corporate tax rate that actually brings more revenue into the federal government so that we can balance our budget and give a better deal to small companies here in New Mexico," Heinrich said, according to the Albuquerque Journal.
Balderas said in the debate he supported lower tax rates for public employees, including teachers and firefighters.