President Obama chose General Electric?s Jeffrey Immelt last month to lead the Council on Jobs and Competitiveness.

So Fortune asks an obvious question: How has Immelt performed in 10 years at the helm of GE?

Plenty have called for his head. A “disaster” is the description used by MarketWatch columnist Brett Arends, Seeking Alpha columnist Steven Towns, and many stock market bloggers. But no major shareholder has attacked Immelt publicly. No proxy advisory firm has told clients to vote against him as a director. The board is officially mum, but people close to the directors say he still has their confidence. Director A.G. Lafley, Procter & Gamble’s former CEO, is showing his support in the sincerest way: SEC filings show that in January he bought 25,000 shares of GE. Still, Immelt’s record isn’t one that anybody, not even this board, would want. When he got the job on Sept. 7, 2001, GE stock was $40 a share. Almost 10 years later, it’s around $20. The company’s credit rating was AAA, the best, awarded to only a handful of enterprises; no more. It was the most valuable company on earth, commanding the highest market capitalization. Today it’s about No. 8 (its rank varies day by day), just behind Royal Dutch Shell.

But what?s more important for a CEO: Leading a company successfully, or pursuing an agenda featuring ?overlapping interests? with the president?