Normally, when the President announces his pick for a Supreme Court vacancy, it is the nominee's day. No other nominations are put forward at the same time except in the rare case of a double vacancy on the Supreme Court. But I think Obama should go in the opposite direction from this tradition, and fill a bevy of available positions with judges from a variety of different backgrounds.
Currently there are 15 Circuit Court of Appeals judge positions and over 50 District Court judge positions open and waiting to be filled. Obama has nominated three Circuit Court of Appeals judges, but twelve seats remain open for nomination. Imagine the powerful presentation that it would make if Obama were to walk out onto the White House lawn not just alongside one Supreme Court nominee, but flanked by a dozen Circuit Court of Appeals nominees and maybe some District Court nominees as well representing the entire panoply of American diversity, both in culture and in personal experience. Intimate -- without outright saying -- that these Circuit Court nominees are the stock from whom future Supreme Court nominees will come. America would cheer.
Of course, no matter who Obama nominates, there will be those who consider themselves slighted, and those in the political opposition who will disingenuously fan whatever flames of discontent they can find. But a mass nomination announcement would short-circuit those efforts. The right wing would have fits, over both the perceived left-wing character of the nominees (which they would whine and moan about no matter who the nominees were) and over the fact that they weren't a bunch of white Christian men.
I'd even say throw the wing-nuts a bone. Put someone one the Fifth Circuit for example (which covers Texas, Louisiana, and Mississippi, not states where Obama is going to be plumbing for reelection votes anyway) who is an openly gay Latino (or Latina) Labor lawyer so far to the left that he or she makes Noam Chomsky look like Gore Vidal. Let the Righties work themselves into a frenzy unloading all their bile on that nominee while the rest of the country makes a collective shrug because most people could care less about a Circuit Court judge for a part of the country where they don't even live.
A day of mass across-the board nominations would remind America that Obama is indeed a larger-than-life figure, a man of big ideas and big execution of them. And it would send the right scurrying against themselves in a bid to prove how narrow-minded and intolerant they are.