SAMMAMISH, Wash. — It is the stuff of liberal fantasies: a vast, defiant territory, sweeping along the country’s Pacific coastline, governed by Democrats and resisting President Trump at every turn.

A single election in a wealthy Seattle suburb on Tuesday could make that scenario a reality, handing the party full control of government in Washington State — and extinguishing Republicans’ last fragile claim on power on the West Coast. The region has been a rare Democratic stronghold on an electoral map now dominated by vast swaths of red, and Republicans’ only toehold on power there has been a one-seat majority in the Washington State Senate.

The prospect of such far-reaching autonomy for Democrats, who already hold all three governors’ offices as well as both houses of the legislatures in Oregon and California, has infused extraordinary energy into what might have been a low-key special election. The race is on track to draw more than $9 million in campaign spending, a record-breaking sum for Washington State. National environmental and abortion rights groups have mobilized, business associations and oil companies have poured in money, and a former vice president, Joseph R. Biden Jr., has intervened on the Democratic side.

Sharon Nelson, the Democratic leader in the Washington State Senate, conveyed the party’s grand aspirations in an almost Trump-like phrase: “A blue wall,” Ms. Nelson enthused, “from the Canadian border to the Mexican border.”