Readers have to get halfway into the Associated Press report on its new AP-GFK poll to find this out, but Barack Obama’s job approval numbers have cratered in the shutdown. His overall job approval is now 37/53, and a majority want Obama to start cooperating more with Republicans, as 63% want Republicans to meet Obama part-way, too:

Americans are holding Republicans primarily responsible for the partial government shutdown as public esteem sinks for all players in the impasse, President Barack Obama among them, according to a new poll. It’s a struggle with no heroes. … Most Americans disapprove of the way Obama is handling his job, the poll suggests, with 53 percent unhappy with his performance and 37 percent approving of it. Congress is scraping rock bottom, with a ghastly approval rating of 5 percent. Indeed, anyone making headlines in the dispute has earned poor marks for his or her trouble, whether it’s Democrat Harry Reid, the Senate majority leader, or Republican John Boehner, the House speaker, both with a favorability rating of 18 percent.

The amusing headline in this instance is “GOP gets the blame in shutdown.” However, the data shows that plenty of blame is being heaped on all sides, by all sides:

— Sixty-eight percent said the shutdown is a major problem for the country, including majorities of Republicans (58 percent), Democrats (82 percent) and independents (57 percent). — Fifty-two percent said Obama is not doing enough to cooperate with Republicans to end the shutdown; 63 percent say Republicans aren’t doing enough to cooperate with him.

Only 30% approve of raising the debt ceiling, clean or otherwise. And despite the best (that is to say, most malicious) efforts of the National Parks Service, more than 80% have had no impact from the government shutdown. That’s not exactly the kind of momentum Obama and the Democrats hoped to generate for pressure on Republicans, and their “no negotiations” stand is practically designed to backfire, if this poll accurately reflects public temperament.

Maybe that’s why Obama has “invited” House Democrats to the White House tonight:

House Democrats have been invited to meet with President Barack Obama Wednesday evening. “Members of the House Democratic Caucus are invited to a meeting with the President today, Wednesday, October 9 at 4:35-5:35pm at the White House,” an email from the White House to House Democrats reads.

The original report read “summoned” rather than invited, but the latter version reflects the e-mail more accurately. Shortly after this Politico report, Fox’s Chad Pergram reported that all four Capitol Hill caucuses would get invitations to meet with the President:

Obama to invite all four Congressional caucuses/conferences to WH this week to discuss #shutdown & debt issues. — Chad Pergram (@ChadPergram) October 9, 2013

Looks like Obama is about to ditch the “no negotiations” strategy. It’s also possible that he may want to give one try to talking around Republican leadership, but I don’t think that the rank-and-file in either GOP caucus will decide to dump John Boehner and Mitch McConnell in favor of President No Talks Until You Surrender. We’ll see.