You have a basic right as a tenant to privacy and enjoyment of the premises you are renting - you're paying rent in exchange for the use of the property during this time. The landlord always has to get your consent before entering (unless it's an emergency) even if they give you 24 hours or more notice. You can't unreasonably withhold consent, but you can insist on reasonable times for the apartment to be available - entire days, and 48 hours in one week, is not reasonable. In this case the burden is on you to give verbal and written notice that you do not consent to the proposed schedule.
Here's the relevant section of Washington Law (RCW 59.18.150):
"(6) The landlord shall not abuse the right of access or use it to harass the tenant, and shall provide notice before entry as provided in this subsection. Except in the case of emergency or if it is impracticable to do so, the landlord shall give the tenant at least two days' written notice of his or her intent to enter and shall enter only at reasonable times. The notice must state the exact time and date or dates of entry or specify a period of time during that date or dates in which the entry will occur, in which case the notice must specify the earliest and latest possible times of entry. The notice must also specify the telephone number to which the tenant may communicate any objection or request to reschedule the entry. The tenant shall not unreasonably withhold consent to the landlord to enter the dwelling unit at a specified time where the landlord has given at least one day's notice of intent to enter to exhibit the dwelling unit to prospective or actual purchasers or tenants. A landlord shall not unreasonably interfere with a tenant's enjoyment of the rented dwelling unit by excessively exhibiting the dwelling unit."
Seattle Housing Code (SMC 22.206.180) states:
"A. Except as otherwise specifically required or allowed by this Code or by the Residential Landlord Tenant Act, chapter 59.18 RCW, it is unlawful for any owner to: [...]
"6. Enter a tenant's housing unit or premises except:
"a. At reasonable times with the tenant's consent, after giving the tenant: [...]
"(ii) at least one (1) day's notice for the purpose of exhibiting the dwelling unit to prospective or actual purchasers, mortgagees, tenants, workers or contractors..."
If you don't protest when the landlord gives you notice, I think legally you are giving consent. You need to write a polite but firm letter to your landlord, and send it by certified mail as soon as possible. Also email a copy with a note that you've mailed a letter if you have the email address, or call and tell the landlord that you find the times scheduled to be unreasonable and that you've sent a letter informing them that you do not consent to the current schedule. I think you can also give a copy in person to the landlord, but whatever you do send a copy by certified mail as proof.
The Tenants Union of Washington State has updated their site, and it includes this Information on Privacy Rights with a sample letter. You'll need to alter their sample for your situation; make sure you emphasize in the letter that having 48 hours of apartment tours a week is unreasonable, that it interferes with your enjoyment of the premises, and that you do not consent to the current schedule. Also cite the state and city laws - you don't have to, but it's a good idea.
I think it's good to be firm and cite as much of the relevant law that backs you up, but make it clear that you are willing to negotiate. You can propose times that you would consent to having the apartment available for viewing and/or you can say that you want to negotiate a mutually agreeable schedule. Whatever you and the landlord agree upon, make sure you still get written notice from them with the exact dates and times they will show the apartment.
You should also call the Seattle Department of Planning and Development - try the Code Violation Line: (206) 615-0808. They might contact the landlord on your behalf, but I think in this situation they can only give you advice. In the DPD's Information for Tenants publication (page 3) the section on Harassment states that you should call the police if the landlord tries to enter without your consent; I'm not clear on whether that applies after you've filed a complaint with DPD or just after you've given notice that you don't consent to the viewing schedule.This DPD memo on Seattle Property Owner and Tenant Rights and Responsibilities has pretty much the same info but includes a list of local organizations and resources at the end.
You probably don't want to start out by calling the cops, but you might want to mention in the letter you send to the landlord that you will be forced to call the police if they don't respect your rights and that you will follow up in small claims court. If your landlord is a complete asshole and enters your apartment without your consent after you contact them, you'll need to call the SPD non-emergency number: (206) 625-5011. That way you'll have official record of the violations.
Another option you may want to consider: you can allow the landlord to have entire days to show the apartment, as long as they compensate you financially. Pro-rate one day of your monthly rent, for example, or ask for whatever it would cost for you to work somewhere else for a day - whatever you think is worth you opening up the apartment. If you pursue this you'd want to get a signed contract in writing first - I don't know enough about contract law requirements, but it should have simple, clear terms about what access you are granting in exchange for what compensation, and probably be notarized or witnessed. The King County Law Library probably has some information that would help if you want to go this route.
On a related tangent, if you leave the apartment while the landlord is showing it, don't leave any valuables around - my friend had an ipod and some other stuff stolen when her landlord had an open house at the apartment she was moving out of.