Unless the "papers" include a document entitled "summons" and another document entitled "complaint ...", you may not have actually been served with a lawsuit.
Some collection agencies try to scare people into paying by sending the people official-looking documents that are not actually official.
In general, the time to start counting is the day after you were served. Counting days for legal purposes can sometimes be subject to dispute. There are several cases that go to the WA Supreme Court involving how to count days.
There are statutes of limitations for every civil cases in WA. Most of the statutes are in Chapter 4.16 RCW (Limitation of actions) at http://apps.leg.wa.gov/rcw/default.aspx?Cite=4 .
Some unscrupulous servers and even attorneys do file documents certifying service on dates and places that did not happen.
Your best course of action is to immediate review your specific facts with an attorney. You or your attorney should at least file a notice of appearance. Filing the notice generally will give you a few more days to answer the complaint. Once a notice of appearance is timely filed, the plaintiff cannot get a default judgment without noting a hearing.
There is typically a statute of limitations on debt but it is different depending upon which state you are in. To be honest, I'm not sure what it is in Washington.
You have 20 days from the time you were served with the paperwork. You can probably "Google" a search query like "example answer to a complaint" and use it as a guide for your response. You want to make sure you file that response with the court before the deadline.
By the time a person is sued for unpaid medical bills, he or she usually has a lot of financial problems. You can try to address each of the problems individually by defending each lawsuit or attempting to negotiate a settlemt of each debt, and there are some reasonable do-it-yourself resources that can hekp you defend yourself. However, most people find it difficult to do what a lawyer does. When they try, it often leads to frustration and in some case can cost ypu more than it would cost to hire an attorney. Maybe you need to consider a bankruptcy case to get rid of all your debts in one step. (There are some debts which cannot be discharged through bankruptcy, but you can certainly get rid of common medical bills.)