No, Rancher does not have a main support phone number. Because we do not believe in having our customers go through unnecessary phone trees and a first-level support that is a mere pass through in many orgs.
Rancher is committed to responding to tickets well within the response time SLAs. High severity tickets (Sev1 and Sev2) trigger internal notifications and SMS alerts via PagerDuty. And, a Support Engineer responds asap via the ticket with an offer to get on a screenshare session to troubleshoot the issue. Our Support Engineers, right from the first response, are highly technical by training and experience.
That said, should there be an exceptional need for you to escalate on a ticket, we request that you directly contact your Account Executive or Customer Success Manager. As required, they can engage any (or all) of our Leaders for Support, Customer Success, and Engineering to help you.
Besides reaching out to your Account Executive or Customer Success Manager by phone/email, you are also encouraged to ping them via your private channel via Slack, if you happen to be on the Platinum plan.