The survey, conducted by researchers from the University of Southern California, Cal State Long Beach and Cal Poly Pomona, found that Democrats hold slim leads over Republicans in four of the state’s six most competitive congressional districts. It also shows three GOP incumbents — Rep. Michelle Steel, in the central Orange County seat CA-45, Rep. Ken Calvert, in the Inland Empire seat CA-41, and Rep. Mike Garcia, in the north Los Angeles County district CA-27 — either trailing or virtually tied with Democratic challengers.

In the U.S. House of Representatives the GOP currently holds 220 seats and Democrats hold 211, while four seats are vacant. If the new survey results hold over the next two months California voters could be a key to flipping the House from red to blue.

But the numbers also show that’s a big if.

The survey of 3,700 voters — conducted from Sept. 14-21 in eight House districts across the state — has a 4.3% margin of error. That’s bigger than the difference in any of the closest races and suggestive of a possible statistical dead heat. The survey also includes data from voters who are undecided but leaning toward one party or another, suggesting that any Democratic gains could depend on particularly strong turnout in November.