With gas prices these days, a flight might be just as cheap! But it also depends upon your timing. You'd want at least 2 days to make the journey by car from Seattle. A friend of mine used to do it pretty regularly and spent the night in Yreka or Weed to break it up pretty evenly. So add the cost of a motel room, too.
If you fly, you can take either Alaska or Southwest, and fly into Sacramento, Oakland, or SFO, whichever gives you the cheapest flight. The car rental could be cheaper out of Sacto, so check it out.
You could also fly into Fresno, but the flights there aren't usually as cheap.