I had trouble today receiving two-factor authentication codes for my two shops. They ended up coming in 30 minutes to 1.75 hours afterwards. I am on Verizon.
Here is another Thread with the same problem.
https://community.etsy.com/t5/Technical-Issues/Security-Code-Not-Being-Sent-In-Time-To-Authorize/m-p...
@UberArt: There have been other reports in this forum with issues receiving the code for two factor authorization (2FA) via text. At the time you set up 2FA you were offered the chance to download a list of backup codes. If you did that, you could use one of those to log in. Even though they are ask for the six digit code, the nine digit backup code will work.