I didn't say anything about the government "functioning." The only place where I think the leadership criticism of a president is valid is in foreign affairs. Maybe also in communicating your proposals to the electorate (you can say what you want, but Obama really flopped when it came to telling people what the ACA actually did).
In the end, it doesn't stop government from functioning (although I still think a Bill Clinton-type figure would've done a better job negotiating Congress), but I don't think discussions on presidential leadership are worth nil.
And although Congressional leadership may be more important, my point stills stands: Right or wrong, voters look to the president for steady leadership, not John Boehner or Nancy Pelosi.