Washington (CNN) -- When Jon Stewart gave Hillary Clinton a career aptitude test on the 'Daily Show' Tuesday night, her answers alluded to a presidential bid -- and she touched on the disintegration of a Middle East cease-fire she negotiated two years ago.
The former Secretary of State, Senator, First Lady and Cabinet member told the Comedy Central host that she wants a home office.
"Do you have a favorite shape for that home office? Would you like it to have corners?" he asked her.
"Fewer corners," said Clinton.
It wasn't lost on the audience that she was referencing the Oval Office in the White House.
In a web-only cut from the interview, she agreed with Stewart that the humanitarian crisis in Gaza is overwhelming.
Palestinians in Gaza are "trapped by their leadership," said Clinton.
"Unfortunately it's a two-pronged trapping," she said. "They have leadership that is committed to resistance and violence and therefore their actions are mostly about how do we get new and better missiles to launch them at Israel instead of saying how we're going to help make your lives better."
Israel's Iron Dome defense system is capable of and successful at shooting Hamas-launched rockets out of the sky, but "that can't be certain" in defending Israelis from bombardment from Gaza, said Clinton, especially now that Hamas is reportedly sending drones over the border.
Clinton pointed to the Muslim Brotherhood, and former Egyptian President Mohamed Morsi, as key allies in the negotiation process between Israel and Palestine that she helped spearhead as Secretary of State in November 2012.
"The Hamas leadership now feels somewhat trapped themselves because they had an ally with the Muslim Brotherhood," she said. "I negotiated the cease-fire with Morsi and Morsi was able to convince the Hamas groups to abide by it. He's gone."
Clinton said that the new, military-led regime in Egypt, which offered a cease-fire Tuesday that Israel accepted and Hamas rejected, sees Hamas as a "danger." Clinton said Egypt's new President Abdel Fattah al-Sisi sees Hamas as a "source of instability and violence that can affect them in Sinai and beyond."
"So they are trapped, and they're trapped I would argue first and foremost by leadership that doesn't really want to make the situation too much better because that gives them a lot of leverage over the poor people in Gaza," she said.
Clinton used her third appearance on the show to promote her new book, "Hard Choices," and Stewart cut her off a number of times.
"I think I speak for everybody when I say no one cares. They just want to know if you're running for President," he said.
"I was going to make an announcement," she said. "But you kind of spoiled it."
"It sounds to me like if I may, you've declared you're running for President," Stewart said.
Stewart referred to two books; 'Clinton, Inc,' a forthcoming book by Daniel Halper, the editor of the conservative Weekly Standard, and 'Blood Feud' by Edward Klein, both of which are critical of her and the Clinton family.
The host also touched on Clinton's testimony over the September 11, 2012, attacks in Benghazi, Libya, that left four Americans dead.
"If you were not running for President, all of this criticism -- there are two books out now that are exposes of the family, there are constant calls for testimony, there are constant parsing of words. If you stopped that tomorrow -- if you said, 'I am not running for President' -- it all stops. Do you agree or disagree?" Stewart asked.
Clinton, who has said journalism is now driven more by entertainment than fact-based reporting, said that "if it all stopped," a lot of people would lose their jobs.
Klein's book, which hinges on multiple anonymous sources to draw a story highly critical of Clinton, recently overtook Clinton's own memoir at the top of the New York Times Best Sellers list.
"I've been amazed at what a cottage industry it is," Clinton said.
To that, Stewart replied -- referring to himself -- "It's just these talking heads sitting around, picking out every little thing -- and making fun of it. It's not right."