Some of the criticisms of President Obama’s handling of the Republicans’ debt-ceiling crisis strike me as more compelling than others. But the weakest is the “Bully Pulpit” argument.

For example, David Frum had a piece, written long before yesterday’s deal, arguing that Obama could have done more to rally the public.

Obama never publicly branded the debt ceiling as “if the Republicans force this country into bankruptcy.” He issued no public call to constituencies like the financial industry to bring pressure to bear on the issue. He did not warn that he would manage any crisis in ways that Republicans would not like. (“If the Republicans in Congress deny me the authority to pay everybody, then I’m going to have to choose some priorities. I don’t think it’s likely that Texas-based defense contractors will find themselves at the top of my list.”)

Instead, he appealed again and again to Republicans’ spirit of responsibility. Good luck with that.

Here’s the thing: Obama and Democrats already fought and won the p.r. fight. The public was with them. The president said an agreement should be balanced, and the American mainstream agreed. The president said the wealthy and largest corporations should be asked to sacrifice, and the American mainstream agreed with this, too. The president urged the public to contact Capitol Hill, and the public responded by crashing phone lines and web servers — twice.

But as we talked about two weeks ago, Democrats only won half the battle, and in the larger context, it’s the half that didn’t matter as much. The White House line proved persuasive, but Republicans didn’t care. Their base was satisfied, and the mainstream could be misled into voting for them next year anyway.

Winning the public-relations fight was no doubt encouraging to the White House, but from Obama’s perspective, it didn’t remove the threat to the nation.

It’s not as if the GOP’s Suicide Squad was starting to show signs of fatigue, and/or hinting at a willingness to give in. On the contrary, Republicans, especially in the House, did the opposite — digging in their heels, welcoming default, and rejecting calls to compromise, even receiving encouragement from their Speaker who no doubt knew better.

Winning a public-relations battle was nice, but the president wanted to avoid a catastrophe that Republicans were willing to cause on purpose. There were multiple points at which the White House could have been more effective, but at a fundamental level, the “Bully Pulpit” didn’t offer a resolution to this mess.

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Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.