PDX - I lost a driver's license on a trip once but I still had credit cards, Costco card, frequent flyer card, etc. Getting my boarding pass was no problem using my credit card and the self check-in. However going through security took quite a while. Even with all my other non state-issued ID, I had to wait for them to call over someone who could handle it, which took forever, then that person had to contact someone in some back room over the walkie-talkie. What they do is they look up your name on Zabasearch or some data base and ask you questions about prior addresses, family members, or other information that only you should know (if you remember).

Oakland - I went through this process with someone else I was travelling with, who only had a paper (newly issued) driver's license, which was evidently not sufficient. It was mostly just an increased security check (bag search and explosives sniffer). That process took much less time.

Again, each of these examples was for TSA. I am not sure how airlines handle it in issuing a boarding pass, but you can now likely issue that through a phone app.

Good luck!