Supporters cheer as Democratic presidential candidate, former Secretary of State Hillary Clinton, speaks during a campaign rally at Sacramento City College on June 5, 2016, in California. GABRIELLE LURIE/AFP/Getty Images

Polls show Democratic front-runner Hillary Clinton leads Vermont Sen. Bernie Sanders ahead of California's important primary vote Tuesday. But the former secretary of state doesn't lead by much.

RealClearPolitics affords her a two-point lead. The site's average of polls gives her an edge of 47.7 percent to 45.7 percent.

The most recent polls have, across the board, found a two-point margin. A CBS News/YouGov poll performed from May 31 to June 3 gave Clinton a 49 percent to 47 percent lead among likely Democratic primary voters. An NBC News/Wall Street Journal/Marist poll carried out over the last three days of May found the exact same 49 percent to 47 percent lead. The final pre-vote Field poll performed at the end of May, meanwhile, found Clinton had 45 percent to Sanders' 43 percent.

RCP Poll Average for Trump vs. Clinton - 2016 General Election | InsideGov

Since delegates are assigned by vote share, the tight California race, coupled with a commanding lead in polls for New Jersey's Tuesday vote, suggests Clinton could soon pass the number to clinch the nomination. She leads among pledged delegates 1,807 to 1,517, according to the New York Times' count and could be taken over the top when superdelegates are considered. Then, she sits at 2,355 delegates overall, and it takes 2,383 to lock up the nomination. California is worth 546 delegates, while New Jersey is worth 142.

While the likelihood of Clinton becoming the nominee is considered a formality by many, the Vermont senator has vowed to keep fighting, and the CBS News/YouGov California poll found that nearly six of 10 Sanders voters in California want him to stay in the race until the Democratic party's July convention. The poll found, however, that 71 percent of California Democrats overall wanted Sanders to drop out for a unified convention, should he not lock up enough delegates to secure the nomination.

Clinton has begun to shift her focus to the likely general election matchup against presumptive Republic nominee Donald Trump. It's currently a tight hypothetical race, with Clinton leading Trump 43.8 percent to 42.3 percent in the RealClearPolitics average of polls.