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The Field Research Corporation poll puts Cruz at 25 percent and Trump at 23 percent among likely GOP voters in the state. Cruz climbed 19 percentage points since the last poll was taken in October. Sen. Marco Rubio clocked in at 13 percent, Ben Carson took 9 percent and other candidates got 6 percent or less.
The poll marks one of the only state-level polls outside of Iowa to show Cruz reaching Trump’s level of support.
California's presidential primary is not until June 7, the last day of contests for the GOP bid. However, thanks to a splintered field and the possibility of a brokered convention, the state's 172 delegates - the largest prize of the nomination process - could be critical for a candidate trying to reach a slim majority.
Cruz has become the front-runner in Iowa, thanks to growing support among tea party supporters and white evangelical Christians. Still, Trump leads almost all recent national polls by double digits, as well as recent polling in New Hampshire.
The Iowa caucus takes place Monday, Feb. 1.