The following is a fact-check of the May 16, 2010 episode of Meet the Press:

SEN. MITCH McCONNELL (R-KY) | Elena Kagan took the position that military recruiters should not be allowed at HLS and the Supreme Court decided 8-0 against that position – TRUE

SEN. McCONNELL: Secondly is the issue of the military recruitment at Harvard.  She took the position that Harvard should not allow military recruiters at the law school, later supported that position in a decision in the–in a, in a case in the court system that ended up with the Supreme Court ruling 8-to-nothing against the position that she took.

So Politifact looked at this one last week when analyzing a statement made by John Barrasso on Fox News. Their research and conclusion (TRUE on both) are sound. Key quote:

The Supreme Court, however, disagreed in an 8-0 ruling on March 6, 2006. The majority opinion, written by Chief Justice John Roberts, ruled against FAIR and, in doing so, rejected the claims of Kagan and the other law professors that the school had the right to enforce non-discrimination policies against the military. “Under the statute, military recruiters must be given the same access as recruiters who comply with the policy,” the opinion said.

Senator McConnell is correct on both, his statements are TRUE.

UPDATE: Here is some interesting additional analysis from commenter wesmorgan1

Special thanks to crowd-sourcer SLBinVA for assisiting with this fact-check.

This fact-check took a combined 15 minutes.