"I think (the White House) feels the president was successful in conveying a new attitude in U.S. leadership, which is very important," Washington Post White House Reporter Michael Fletcher said. "At the same time, facts on the ground remain as intractable as ever."
The Obama administration's biggest challenge will be convincing the Israeli government to halt the growth of Israeli settlements in Palestinian territories, including so-called "natural growth," Michele Dunne, a senior associate and expert in Arab politics at the Carnegie Endowment, said.
"Israel has already shown willingness to dismantle the outposts that consist of a few trailers on a hill somewhere that have not been authorized ... by the Israeli government," she said. "But there are some Israelis who have been there for a very long time where you actually have new generations of people coming up... that's the really difficult issue."
The panelists also told Schieffer why some in the Middle East may not have been happy with Mr. Obama's speech. Hear below this week's edition of "Washington Unplugged."