California voters go to the polls. Getty Images

Democratic efforts to win a House majority in the midterms could hit a snag Tuesday in one of the country's most liberal states. In California, the party hopes to challenge about 10 GOP-held districts and pick up a good chunk of the 23 Republican seats it needs to win control of the chamber. But Democrats need to get past an obstacle in Tuesday's primaries: a system that sends the top two candidates, regardless of party, to November's general election. Strong Democratic candidate recruitment and voter enthusiasm fueled the party's hopes that it could compete in California House districts recently dominated by Republicans. However, the Democratic vote in some swing districts could get fragmented among multiple candidates, leaving the potential for two Republicans to advance.

Local and national party officials acknowledge most paths to Democrats winning a House majority — and pushing for their vision on health care, immigration and taxes — require a strong performance in California. Democrats face the prospect of getting locked out of up to three competitive districts in November, which would reduce the party's margin for error in key districts elsewhere. "It would absolutely be an embarrassment," said John Vigna, communications director for the California Democratic Party, about the prospect of more than one lockout. "We are very cognizant of the role California has to play in taking back the House. I think a lot of our voters are very aware that any chance of Democrats taking the House has to come through a gangbusters performance here in California." Officials from both parties closely following the House primaries generally see the state's 39th and 48th Districts in the Orange County area as the ones where the Democrats are in the most danger of missing out on the general election. Incumbent Republican Rep. Ed Royce is retiring in the 39th, while GOP Rep. Dana Rohrabacher faces a challenger from his party in the 48th. Observers also see some risk for a Democratic lockout in the 49th District, another Orange County seat vacated by GOP Rep. Darrell Issa's retirement. They acknowledge the prospect is less likely there.

Rep. Darrell Issa (R-Calif) at the 2015 WEF in Davos, Switzerland. David A. Grogan | CNBC