I live in Washington State.
The law strictly prohibits a landlord from self-help conduct such as lock-out, cutting off utilities, removing furniture, disabling the dwelling by removing doors, forcible conduct, or any other means. The only way a landlord can require you to vacate the dwelling is by having a sheriff supervise the move after obtaining a court order. The process of getting a court order (eviction) takes about a month or longer if the landlord proceeds as fast as the law will allow. If the 3-day notice was posted on the door, the landlord must also mail a follow-up copy by regular mail, and that adds one extra day for the deadline to pay the rent. If the deadline passes and you still have not paid, the landlord can immediately start the eviction ("unlawful detainer", it's called) which is a court proceeding. The court summons and complaint can be filed with a case number, but an unfiled summons and complaint can also be used, and either way, you must carefully follow the instructions on the summons. Even if you are behind in rent, you may have more defenses than you realize, and you'll need a lawyer to help you evaluate what to do. I'm attaching links to the Tenants Union and the Northwest Justice Project, and you should contact them immediately.
The 3-day notice can demand only rent. If non-rent charges are included, the notice is defective. Some leases define "rent" to include late charges, which is a permitted clause, but if late charges are not specifically included in the definition of rent, they can't be included in the 3-day notice. If the landlord accepts partial payments from you, the landlord can't use that same 3-day notice to start the eviction but has to start over with a new 3-day notice.
This answer is intended as a courtesy only, and does not constitute an attorney-client relationship between the attorney and the questioner.
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Landlord / Tenant Lawyer
I agree 100% with Mr. Stimmel, I am just adding one more resource to his list of referrals.
This answer is for informational purposes only and should not be construed to establish an attorney client relationship. Before taking any legal action, it is always advisable to discuss your specific situation with an attorney.
Only the Court can issue a judgment and Writ authorizing the Sheriff to lock you out. This can only be done after due process has been done in the court system. Self help eviction is unlawful. If your income is low enough, you can get free help down at the Seattle courthouse. The King County Bar Association Housing Justice Project is on the third floor, just to the left of Department W325. If you are outside of Seattle, and south of I-90 go the the HJP at Kent Courthouse, Room 1281.