[cnn-photo-caption image= http://i2.cdn.turner.com/cnn/2010/images/03/17/art.megwhitman.0309d.gi.jpg caption="Meg Whitman's very large lead over Steve Poizner in the battle for the California Republican gubernatorial nomination has dramatically shrunk, according to a new poll."](CNN) - Meg Whitman's very large lead over Steve Poizner in the battle for the California Republican gubernatorial nomination has dramatically shrunk, according to a new poll.
A Public Policy Institute of California (PPIC) survey released early Thursday morning indicates that 38 percent of likely GOP primary voters back Whitman, a former eBay CEO who served as an adviser and surrogate for Sen. John McCain's 2008 presidential campaign, with 29 percent backing California Insurance Commissioner Steve Poizner. A large number of voters, 31 percent, are undecided.
Whitman's nine point advantage is down from a 50 point lead in a PPIC poll conducted in March.
Poizner has attacked Whitman in recent weeks with a barrage of commercials questioning her conservative credentials, her poor voting record, and her links to Goldman Sachs.
One ad claimed Whitman would prolong unpopular Gov. Arnold Schwarzenegger's policies, making that point by showing an image of the governor's face morphing into Whitman's image. Another ad attacked Whitman on the hot topic of illegal immigration and border security, saying that "she supports Obama's amnesty plan."
The billionaire, who so far has spent more than $60 million of her own money on her campaign, is firing back with a new commercial that labels Poizner a Sacramento politician. In the ad she says she'll clean up the mess he's made, and she states that "on immigration, I will secure our border and I'll send in the national guard if necessary. I say no drivers licenses, no sanctuary cities and absolutely no amnesty, period."
The Republican winner in the June 8 primary will most likely face off in the general election against state Attorney General Jerry Brown. The former two-term governor is the presumptive Democratic nominee.
According to the survey, Brown leads Whitman 42 to 37 percent in a hypothetical general election matchup, with one in five undecided. Brown tops Poizner 45 to 32 percent, with 23 percent undecided.
In the fight for California's Republican Senate nomination, the poll indicates that 25 percent of likely GOP primary voters back former Hewlett Packard executive Carly Fiorina, with 23 percent supporting former Rep. Tom Campbell and 16 percent pulling for state Assemblyman Chuck DeVore. Fiorina and Campbell were also deadlocked in PPIC's March poll. DeVore, a favorite of the Tea Party movement, has doubled his support since March, according to the survey.
The winner will face off in November against three-term Democratic Sen. Barbara Boxer. According to the survey, Boxer leads Campbell by six points, Fiorina by nine points, and DeVore by 11 points, in possible general election showdowns.
The poll also indicates than six in 10 of likely California primary voters back a ballot measure that aims to dramatically alter the state's primary process. Less than three in ten say they would vote against the measure, which would allow all voters to cast ballots for any candidate in a primary, regardless of party affiliation. The proposed measure calls for the top two vote-getters to advance to the general election.
The PPIC poll was conducted May 9-16, with 2,003 California adults questioned by telephone. The survey's overall sampling error is plus or minus two percentage points, and plus or minus five percentage points for questions directed only to likely Republican primary voters.
Follow Paul Steinhauser on Twitter: @psteinhausercnn