Generally, I get cards within a week, whether it’s brand new or a replacement. Ic it were urgent, I’d ask for overnite, but since I have many other cards it’s generally not an issue to have it rushed (unless I have a big purchase I am planning to make and want to have the initial spend for a new card met ASAP).
When I have requested overnite, I’ve received the card promptly. We have varying credit limits–seems to vary by issuer–Chase and CapOne have 5 figure limits for us while all the others have 4 figure limits.