First of all, they claim that he's "negotiating with terrorists," which you are never supposed to do (we'll put aside the argument about how, in divided government, he's supposed to avoid that constitutionally). Their point, which I'd have to agree with, is that the Republicans don't want to negotiate or compromise. But their conclusion is that it is therefore pointless to try.
So then, you have to ask what the alternative is. Here's Michael Tomasky explaining it as well as anybody has.
Here, for example, is something that actual adults in the room do. They say at the outset: This is not a negotiation; this is a hostage situation. The House and Senate have voted 11 times since 1997 to raise the limit. Every time, they’ve groused, especially members from the party out of power; some people vote against it, as Obama himself mistakenly did once, but even then, the vote has been symbolic, with the winking understanding that it will pass; and onerous conditions like these are never attached to such votes. So this is unprecedented and illegitimate. If Obama’s as good at swaying public opinion as the conjurers say he is, he would have swayed it on the debt ceiling back in May.
What this misses is the first point...Republicans were never going to negotiate or compromise. We've seen that neither the voters, nor the President, nor other Democrats, nor sane Republicans, nor their Wall Street donors have been able to convince them to move one inch. So you'll have to explain to me why this approach would have led to any different outcome than we're facing right now.
The only difference we would have seen if the President had followed the advice of the poutragers is that he would have had no case to make to the American public that he was any different in how he approached this than the Republicans. Certainly the public is very attracted to the idea of "a pox on both your houses" in these kinds of situations. But President Obama has not only bent over backwards in trying to avoid this, he's given over half a dozen press conferences in the last couple of weeks to attempt to sway the media narrative and he went on TV last night to take that message directly to the American people (bully pulpit anyone?). In a game where the Republicans seem content to shoot the hostage, I can't think of another strategy I would prescribe. He's played the card he has - even calling for the public to let Congress know, thus apparently shutting down phone systems and servers last night - and is now banking on US being adults as well. We'll soon see if the American public is up to the challenge.