She tells The Early Show co-anchor Rene Syler we can expect sparks to fly on Capitol Hill, once President Bush makes his pick known.
"This is a difficult moment for the White House because any nominee that would make the conservatives happy, (who would) be the pick they have hoped for so long, is going to be quite upsetting to the Democrats," she says. "Everyone knows this is the critical seat, this moment to replace Justice (Sandra Day) O'Connor, the swing vote, the justice in the middle whose vote on these cases makes such a critical difference.
"So, this is going to be a fight. But at the end of the day, the White House concluded they were going to have a fight to get Harriet Miers confirmed, a fight they did not expect. So now, they're ready for a fight, a more traditional fight, with Democrats."
What's more, Greenburg says, the new name could be known shortly.
"My sources (Thursday) said it could be as soon as (Friday)," she says. "That looks unlikely, but I would expect by Monday. My sources tell me the White House has identified a leading candidate. They've looked at a small group of federal judges.
"Advisers are suggesting to President Bush that he turn to an experienced federal appeals court judge with a clearly defined judicial philosophy. They feel they learned that from the mistake of the Miers nomination. The American people and the senators want an experienced judge who can articulate his or her views on the law."
The dynamics could be different in another way, Greenburg observes: "The White House does not feel as compelled to nominate a woman or a minority as it did when it originally began thinking about this nomination.
"My sources tell me Janice Rogers Brown, Edith Brown Clement are not under consideration, nor is the attorney general, Alberto Gonzales. The spotlight now is on a federal appeals court judge from New Jersey, Sam Alito, another judge from Virginia, Michael Luttig. Priscilla Owen also in very much in the mix, and the decision will be made very swiftly."