The government must function. Honestly this is better for you guys then if he died with the burn as prez.
I am not a Republican. I don't vote Republican either.
The Supreme Court will function just fine with 8 members. It routinely hears cases with 8 Justices. All the cases this term will have to be decided by the current 8 members. A hypothetical new Justice would only be joining in conferences to decide on taking cases, you do not need 9 Justices for that. Scalia was over emergency appeals for the 5th, the Chief Justice or another can easily step in to fulfill that role.
The Supreme Court will function just fine without an appointment.
As for a recess appointment, the GOP will continue to do what they have been doing and that is having pro forma sessions during recess. They have been doing this to prevent Obama from making recess appointments for awhile now, so there's little doubt they will stop doing so now. Not to mention, a President hasn't done a recess appointment for SCotUS since Eisenhower.