Arlen Specter was not “selected by leaders in Washington.” He selected himself. As one of the last of the moderate Republicans, he was headed for defeat in his own party’s primary. He thought (no doubt correctly) that his chances for survival would be better in the other party, so he switched. The White House promised him support because his vote was an absolute sine qua non for overcoming Republican filibusters, most crucially filibusters against the health-care bill, on which the fate of Obama’s Presidency and the Democratic Congress rested. If this was a “backroom deal,” it was one that the White House and the “Democratic establishment” would have been criminally irresponsible not to cut.
I'd add that the White House does lose some credibility here in its ability to woo GOP defectors -- which it may well need in upcoming years as the party moves rightward and strands the remaining moderates. On the other hand, as Hertzberg argues, the White House was probably better off with Sestak winning. It only needed to make a credible show of standing up for Specter to avoid the charge of casting him aside after he was no longer useful.