Appearing on CBS News' Face The Nation Sunday, Axelrod said "grave concerns" had been raised about such a possibility, and that because discussions at the White House are still ongoing, President Obama has not made a decision on the matter.
"One of the most heartening things about the speech was the kind of reaction that it got across the region, from Arab leaders, from Israeli President Shimon Peres and others in Israel," he said.
Guest moderator Harry Smith noted that Israeli prime minister Bibi Netanyahu did not support a halt to settlements, and Axelrod admitted that the peace process is "difficult."
Axelrod also predicted major healthcare reform will be accomplished this summer, and while he admitted it would be expensive, he warned of far worse if action isn't taken.
"If we don't do health care reform, if we don't get costs under control, if we don't reform the system, then we will have a fiscal disaster in the future," he reasoned.
Axelrod also said there are signs of progress in the economy, and that the stimulus plan is just gaining "momentum."
He said he would not pre-judge the impact of the latest stimulus plan and would not say whether President Obama will have to go back to Congress to ask for more money.
More from Face The Nation (6.07.09):
To watch David Axelrod click on the video player below.