Although Clinton once had a commanding 12 point lead in the Golden State in January, the New York senator has just a two point lead, 36 to 34 percent, ahead of Obama, the junior senator from Illinois, The San Francisco Chronicle reported Sunday.
On the Republican side, Arizona Sen. John McCain has widened his lead in the state GOP primary, with 32 percent support among likely voters, compared to the 24 percent of former Massachusetts Gov. Mitt Romney.
With 18 percent of Democratic voters still undecided before Tuesday's primary, the election is still up for grabs, said Mark DiCamillo, the poll's director.
"It's an unusually volatile election, with a very high number of undecided voters and so many moving parts," he said. "It could be a very, very close election."
The poll, conducted Jan. 25 to Feb. 1, was based on a telephone survey of 511 likely voters in the Democratic primary and 481 likely voters in the Republican primary.
The margin of error is 4.5 percentage points among Democrats and 4.6 percentage points among Republicans.