Meantime, as the co-chairman of Obama's intelligence advisory board, Hagel wants him to start negotiating with the terrorist Palestinian movement Hamas which does not think Israel has any right to exist.
The White House has mounted a major lobbying effort of its own to counter Hagel's critics, but thus far with mixed success.
"I don't think the president can afford to lose another skirmish," Abraham Foxman, president of the Anti-Defamation League, a leading Hagel critic, said this week.
Foxman has been heavily lobbied by the West Wing in the past week to support Hagel's nomination. But in a carefully worded and subdued statement Monday, he said:
"Hagel would not have been my first choice, but I respect the president's prerogative."
Responses from other Jewish groups less muted. David Harris, director of the American Jewish Committee, was reported to have told an administration official that he was keeping its powder dry: "We're going to be watching the Senate confirmation hearings, listening carefully, and we'll determine then our position."
Some Democratic leaders, too, seemed to be less than enthusiastic in their responses. Sen. Charles Schumer of New York said Hagel "has earned the right to nothing less than a full and fair process in the Senate. I look forward to fully studying his record and exploring his views."
And there's also Hagel's mixed record on sanctions toward a nuclear-armed Iran. He's embraced international sanctions against its threatening uranium-enrichment that has led to the brink of nuclear weapons development. But he hasn't drawn a clear red line in the sand as Defense Secretary Leon Panetta did, signaling a potential military response if Iran doesn't abandon its path toward nuclear missiles.
Brennan's actions as Obama's senior adviser have also raised questions about his approach to the deadly use of missile-armed drone aircraft that have effectively struck terrorist targets. It has been widely reported that Brennan has sought much more stringent limits on their use, which Panetta and his successor at the CIA, David Patraeus, escalated over the past several years.
Republicans are holding their cards close to their vest on both nominations and there may be more opposition to their confirmation as the hearings begin. But GOP leaders are signaling that this will not be a slam dunk for Obama.
South Carolina Sen. Lindsey Graham said Obama's decision to name Hagel was "an in-your-face nomination."
Senate Republican Leader Mitch McConnell said Hagel would be given a "fair hearing", but added that the central question which needs answering is, "Do his views make sense for that particular job?"
Newly-elected Texas Sen. Ted Cruz, among other GOP senators, had already made up his mind before Hagel was chosen, saying it's "very difficult to imagine a circumstance in which I could support his nomination."
Sen. John McCain of Arizona, who has been one of the president's most relentless national security critics, has problems with both nominations, saying he has "many questions and concerns."
Obama is dramatically reshaping the direction and tone of our nation's national security team. In choosing Hagel, Brennan and Massachusetts Sen. John Kerry to become secretary of State, America's defense and foreign policy is shifting sharply further to the left.
This team would probably "look long and hard, adopt a 'look before you leap' approach, before committing U.S. forces and prestige to foreign lands," said former State Department official Karl Inderfurth who worked in the Clinton administration.
But with al Qaeda affiliates and cells sprouting across North Africa, the Middle East and elsewhere, is that the signal we want to send to our enemies?