Fox News misled on the current budget negotiations with the canard that President Obama was more willing to meet with Iranian President Hassan Rouhani than meet with congressional Republicans, though Obama has said publicly that he will work with the GOP on reasonable budget proposals and it is not confirmed that he will meet with Rouhani. 

On the September 23 edition of Fox & Friends, co-host Steve Doocy attempted to obscure the debate over the looming government shutdown with a misleading analogy, citing reports that Obama might meet with Rouhani and contrasting them with Obama's supposed unwillingness to “meet with Republicans to discuss and negotiate over the debt limit.” Fox News legal analyst Peter Johnson Jr. repeated the allegation, calling the president's approach “topsy turvy” and claiming he needed to “focus on the real enemy.” Fox then aired a brief clip from Obama's August 20 speech at the Ford stamping plant in Liberty, Missouri, claiming the speech demonstrated that Obama was more interested in attacking the GOP than working with them.

In fact, during the same speech, Obama emphasized his willingness to work with Republicans to find a reasonable compromise on the debt ceiling and budget:

Democrats and some reasonable Republicans in Congress are willing to raise the debt ceiling and pass a sensible budget.  And I want to work with Democrats and Republicans to do just that.

White House Press Secretary Jay Carney also explained Obama's willingness to negotiate on reasonable budget proposals (emphasis added):

So I think what the President said goes to what we've been discussing earlier, which is, when it comes to reaching a broader budget agreement, the President has consistently been willing to seek common ground and to make reasonable concessions to Republicans and to their priorities.  What he has not been willing to do is stick it to the middle class in order to achieve some of their ideological agenda priorities, and reach a compromise that benefits the wealthy and corporations, rewards insurance companies, but doesn't help the middle class -- in fact, hurts the middle class.

Furthemore, the Wall Street Journal reported on September 23 that Secretary of State John Kerry would meet with the Iranian Foreign Minister Javad Zarif at the U.N., but suggestions that Obama may meet with Rouhani remain unconfirmed. As Reuters reported:

White House spokesman Jay Carney has deflected questions all week about whether the two leaders would meet during the U.N. gathering. On Thursday, he acknowledged a change in tone between Iran and the West since Rouhani took office and said a meeting was possible, though one was not scheduled.

“It's possible, but it has always been possible,” Carney said. “The extended hand has been there from the moment the president was sworn in.”

Even if Obama were to meet with Rouhani, the administration has been clear that Iran must abandon any nuclear program. From Reuters:

Carney reiterated that Obama would be willing to have bilateral negotiations provided the Iranians were serious about addressing the international community's insistence that Tehran give up its nuclear weapons program.

“That is the position we hold today,” Carney said.