According to state estimates, Washington gained more new residents (careful, link goes to a pdf) from natural increase than from migration between 2000 and 2004. (For you data geeks out there, it’s about 138,000 new residents from natural increase—births minus deaths—and 134,000 from net migration, which is typically to and from other parts of the U.S.) The trend of more births than new migrants was particularly strong in King County, Seattle’s home, which gained four times as many new residents from natural increase as from migration.
In one way, the fact that births outpaced migration shouldn’t be surprising: the economy wasn’t exactly going gangbusters for most of the past quadrennium, and high unemployment rates may have kept away some newcomers.
But in another way, it is a surprise. Like the country as a whole, Washington is at a temporary birthing lull. The baby boomers have largely aged past their reproductive peak, and the relatively scanty "baby bust" generation of the 1970s has entered theirs.
So it was a slow period for both births and migration—which means that the four years from 2000 to 2004 saw among the slower rates of population increase for the state in recent memory—just a little over 1% per year. However, "slow" for Washington is still very, very fast—fast enough to double the state’s population in just a little over 60 years, well before today’s toddlers reach retirement age.