Sean Trende does an historical analysis of open primaries, such as Washington now has and finds the following:
[T]hese primary elections end up looking an awful lot like the November elections. I gathered the results for congressional and senate primaries in recent years where Washington used the blanket primary system (1992-2002 and 2008). This gave me a nice dataset of 65 elections. I looked at the total Democratic vote cast in the primaries, and compared it to the total Democratic vote in the general election.
On average, the Democratic candidate improved his or her share of the vote by only 1.5 points from the fall election. And there aren't too many outliers. In 47 percent of the elections, the Democratic share of the vote in November was within two points of the Democratic share of the vote in the primary (for those who speak "geek," the standard deviation is a reasonably narrow 4.2).
And most of the outliers came in 1998, when the Republicans' drive for impeachment caused a late swing against them; the average Washington Democrat saw his or her vote share improve by 4.2 points that year, almost three times the norm. As a general rule, when the Democratic share of the vote rises above 52 percent, the Democratic nominee can feel pretty safe that he or she will win. When it falls below 46 percent, the Republican will almost certainly win.