What would you have the Supreme Court do prior to Barack Obama's officially becoming President-Elect? The designation of anyone other than Barack Obama as President-Elect would create a major crisis of legitimacy, and I see no way of avoiding that.
The only sane remedy I can see would be to invoke the Twentieth Amendment in such a way that Barack Obama would be free to take as long as he wants demonstrating eligibility; if necessary, Joe Biden could serve as Acting President until such time as Barack demonstrates eligibility.
If a public announcement were made that if Barack is eligible he can be inaugurated within hours simply by phoning the Hawaii department of records and authorizing them to authenticate his COLB, I would think that should effectively cause people's anger at the delay to be directed at Obama, rather than the Court or anyone else. The only way to stir up anger elsewhere would be to acknowledge that Barack's birth records don't match his claims, and that would be a dangerous move for Obama.
In a sense that is what the 20th Amendment seems to imply, but will those who are supposed to do that invoking actually do the invoking????