According to Article II, Section 2 of the U.S. Constitution President Obama can make a recess appointment, since Justice Scalia died during a recess. President Obama could make an appointment, which would take effect immediately.
Despite having to be done so quickly (probably this week), I feel that it would actually show respect to Justice Scalia who was so dedicated to the Constitution as written, and to the Court, by allowing them to continue to do their work without being short a Justice.
The appointment would still be subject to Senate approval.The Senate would have till the end of the year to confirm the nomination.
President Eisenhower made just such an appointment in the election year during which he was seeking re-election.