Last year, both the Republican and Democratic contests were pretty much locked up by the time Golden State residents cast their votes in June.

It's not clear how other states would respond if Senate Bill 568 is passed and signed into law. But the legislation would let the governor move California's primary even earlier if other states change their election dates.

Lara says the change would also help increase voter turnout, and not just for presidential contests: The bill would also move up statewide and legislative race primaries.

In 2008, California saw its highest primary turnout in 28 years, after moving up its presidential primary to February. But state leaders reversed course before the 2012 race, saying it was too expensive and complicated to host the earlier voting. (You can learn more about California's shifting primary dates here.)

Lara said having a seat at the table is too important to miss.

"California is the largest, most diverse state in the nation with one of the largest economies in the world,” he said. “Yet Californians’ voices are silenced when it comes to choosing presidential nominees. California is leading the nation on clean air, criminal justice reform, and expanding health care for all, and moving up our presidential primary will ensure our state’s voters are heard in the national debate.”