If there were any lingering doubts about who got the better of last week’s Question Time session, this should settle them.

The White House has suggested that it would like Obama to address the Senate GOP Conference, with TV cameras present. Obama administration officials are eager for voters to see Obama operate in a format he relishes — and handle his former Senate colleagues the same way he did last week to House Republicans at their annual retreat…

“They don’t want anything to do with it,” said a GOP insider. “They want the whole thing to just go away.”

Republicans have considered several different formats for any session with Obama, including a “roundtable discussion,” but don’t believe that it will benefit them politically if Obama comes off as well as he did in Baltimore…

Cornyn acknowledged that Obama was “in his element” in his meeting with House Republicans.

“I can see why he and his handlers would want to replicate that,” Cornyn said. “I think we’re more interested in serious public policy issues rather than providing another photo-opportunity for the president.”

The One said last night at that fundraiser that he’s ready to “call on Republicans” to have them present their ideas, so his confidence appears to be up. In all candor, when I think about it, there aren’t many Senate Republicans I’d be eager to see going one on one with him. Coburn or Kyl could make things interesting, and Graham can be a pitbull during Senate questioning of cabinet officials, but who else is ready to stand in there? Thune, maybe? The pickings are slim, my friends.

Update: From National Journal’s poll of “political insiders,” 82 percent of Democrats think their party would benefit from another Question Time session. Among Republicans, just 46 percent think so compared to 52 percent who say it wouldn’t. Sample quotes:

“It was a stupid decision to allow the Q&A to be televised. Obama wiped the floor. We are still not that good at messaging. I think our leaders start to believe their own press releases. We are the same party the voters rejected in ’06 and ’08.”

“Talking policy is the wrong move: Republicans just need to oppose President Obama.”…

“Whether GOP leadership gets it or not, we do not yet have a member or members capable of scoring significant points in this format.”

“He’s better at it than we are: Obama has the ability to make the Democrats appear reasonable; Reid and Pelosi do not. We want more of Reid and Pelosi.”