If investors aren't totally naive, and if they do understand that many House Republicans leaving today's meeting are dead-set against any "clean" debt limit increase, maybe they're assuming that Republicans will admit defeat. There was some of that tone in the on-camera briefing following the meeting, probably the leadership's last appearance in front of the press before a staged meeting at the White House.
"What we want to do is offer the president, today, an opportunity to move," said John Boehner. "I would hope that the president would view this as an opportunity and a good-faith effort to meet him halfway."
That framing was perfect for TV, until TV reporters (CNN producer Deirdre Walsh is really good at this) asked what Boehner wanted to get out of the CR. "That's a conversation we're gonna have with the president," said Boehner. In other words, "meeting halfway" meant punting on the debt limit for six weeks, and using that time to keep negotiating on the CR as the government remains shut down. It's "halfway" in the sense that Democrats have demanded that the Republicans agree to something clean before any negotiations begin. But Senate Democrats had specifically asked for the government to open before they started talking.
Let's not understate how hard it is to punt on the debt limit. In January, Republicans began this whole strategy of staggering "leverage" points across the year with the "No Budget, No Pay" Act. That bill raised the debt limit for four months on the condition that the Senate passed a budget—ostensibly to start an actual budget conference with the House. (We know how that ended.) And that bill passed only because Democrats endorsed it. Thirty-three House Republicans opposed it. It's up to Democrats to decide whether to bail Boehner out again, and whether doing so would make the "clean CR," that chimera, more or less likely.
On Boehner's side: the White House. Sure, this isn't exactly what Democrats want. But the administration has not opposed a "clean" short-term extension of the debt limit. It's harder for other Democrats to oppose Boehner's gambit if the White House is approaching it as the start of a deal.