I have a very recently issued Nevada driver’s license that’s probably “enhanced” but that’s the only ID I have on me. I forgot my passport at home. I’m in anchorage now and the cruise leaves this evening. It doesn’t make any stops in Canada except the final destination of Vancouver in one week. Then I’m flying direct from Vancouver to my hometown of Las Vegas. How screwed am I? Is there any way to salvage the trip? Could I maybe pick up a replacement passport from the Vancouver consulate if I visited a passport office in Anchorage now? Should I leave the ship at the last US stop and just book a new flight from there? Why doesn’t CBP just have all the contents of all the passports in a searchable database so there’s no need for obsolete paper documents?
I think you're out of luck for today.
As Richard mentioned, your driver's license is not enhanced, so it really doesn't help you at all.
The usual thing to do in this situation would be to go in person to a passport agency, where a passport can be issued the same day. Unfortunately, there are none in Alaska, and I doubt you have time to fly to another state, stand in line for hours, and fly back.
You may as well call the cruise line and ask if they will let you on, if you promise to get off at a US port; but I wouldn't count on that. Otherwise, I expect they will not let you board. You could also ask for a refund, but I wouldn't count on that either.
However, if you call the cruise line, I would guess they might offer to let you change your cruise to another date, or to credit your fare toward a future cruise on the same line. If you have a few extra days to spend on this trip, you may be able to rebook on a cruise leaving soon that doesn't exit the US. Or, rebook for a cruise to Canada in a few days, and have someone from home fetch your passport and send it to you via overnight shipping.
(Anything involving the US consulate in Vancouver is unhelpful, since Canada won't let you enter in the first place without a passport or other accepted travel document. The thing about a CBP database doesn't quite make sense either, since it's Canada that needs to check it. And anyway, beyond the information in the passport, a significant factor in having it prove your identity is that it's physically in your possession; it would take some work for an impostor to achieve that.)
According to the Department of Homeland Security, Nevada does not issues EDLs that can be used to enter the US. Regardless, EDLs cannot be used to enter the US by air.
Furthermore, you will likely be refused entry to Canada, and possibly refused boarding for the cruise (not sure on that, but airlines would typically deny boarding in your circumstance, rather than you being rejected at immigration in Canada). Picking up a passport in Alaska before departure is your best bet, but I would work on the assumption that you will not make it to Vancouver.
Likely they won't let you on the boat without a passport (like airlines). Even if they do, this is going to be a problem entering into Vancouver.
This site indicates that there's a private company able to do expedited passports in Anchorage in 24h, give them a call ASAP to see if they can do it in time.
Be prepared to pay a hefty fee... $500+
Edit: Or pay a friend to fly it to you...
The US government has expedited service. If you are traveling in the next 2 weeks via plane or cruise ship. The cruise line will most likely reject you due to the stop in Vancouver. You cannot enter Canada with only a Nevada license.
It does not look like there are any offices in Alaska. There are ones in Seattle.
Technically you still have a passport -- replacing it will invalidate the first one.
If you have a passport -- have someone get it and FedEx it to you. They can do it to any place including hotels, the cruise ship. Most likely breaking in and repairing the damage may be cheaper than expedited requests.