There will most likely be a public option in the Senate bill. Harry Reid, who will decide what the bill finally looks like, is leaning toward an "opt-out" public option, so that no one in Mississippi is forced to accept government health care to treat their rickets. Olympia Snowe, who will not vote for the health care bill no matter what she tells you but who might vote to break a hypothetical filibuster, prefers a "trigger" public option. "Triggers" are what Congress does when it wants to avoid creating programs or implementing policies without actually officially voting against them. Max Baucus is still being a dick for the hell of it.
Harry Reid thinks he has enough votes to pass a bill with a strong, opt-out public option, and he is like one or two solid votes away from a cloture vote on said bill.
The White House is skeptical of his vote-counting, though, and in a meeting late last week, they pushed him to keep trying to get Olympia Snowe on-board.
This upset Reid, because he thinks the White House should just get his back and announce that they support the thing he wants to do. But the White House doesn't want to openly support anything until passage looks like a sure thing. They are kinda big political babies about that kinda stuff, as Jon Corzine could tell you.
But it was not Obama "pushing" for a stupid trigger compromise so much as it was the White House wanting to make sure Harry Reid really knows what he's doing, because honestly that is always an open question with that guy.