You'll need to go over the details of your case with your lawyer. However, it appears that the answer to your question is that it is not too late. The applicable provision for this seems to be Revised Code of Washington (RCW) 46.20.308(6), which states:
(6) The department of licensing, upon the receipt of a sworn report or report under a declaration authorized by RCW 9A.72.085 under subsection (5)(d) of this section, shall suspend, revoke, or deny the person's license, permit, or privilege to drive or any nonresident operating privilege, as provided in RCW 46.20.3101, such suspension, revocation, or denial to be effective beginning sixty days from the date of arrest or from the date notice has been given in the event notice is given by the department following a blood test, or when sustained at a hearing pursuant to subsection (7) of this section, whichever occurs first.
(Bolding added.) The process starts with the Department receiving a report from the officer as required under subsection (5)(d). The officer generally submits that report within 72 hours after arrest, in which case the suspension starts within 60 days of the arrest and the Department sends out the notice of suspension after getting that report. But the officer has the option under (5)(d) to wait to send that report to the Department until until after the blood test is received, in which case, as the part I bolded above says, the 60 days starts from the date the notice is sent to you about that suspension.
Discuss with your attorney whether contesting this suspension is something worth trying. Absent something unusual fighting a supension for refusing to test is pretty difficult in the states I'm familiar with, and I have no reason to think Washington would be much different on that.