Linux kernel has had support for 64 bit time for years. On Debian, packages for the upcoming release were updated to 64 bit time earlier this year. I’m fairly sure the other distributions have done or are doing the same. So basically you now have 2 years to upgrade your OS and to pester the vendors of commercial software to do the same.

Like someone else said, it will be 2 very busy years, but we can survive this.