Steele also joked that it was way too early to be discussing prospects for 2012. "We're a long way from that? Eighty-six days [into the new administration] and we're already talking about 2012? Can I just get a cup of coffee and relax for just a few more months before we have that conversation?" he laughed.
It was the first time Palin has been to the lower 48 since attending Washington's Alfalfa Club dinner -- featuring Obama -- in late January.
"It drives Washington insiders crazy because they cannot predict what she's gonna do next," said Marjorie Dannenfelser, president of the Susan B. Anthony List, an organization that supports women against abortion rights in politics.
"The message that ought to be pretty clear is that she's not planning her political future right now," Dannenfelser said.
The timing of Palin's trip has been criticized by some in her home state. Alaska's state legislature is just wrapping up its 90-day legislative session Sunday.
Lawmakers have been sparring with the governor over whether to accept federal stimulus money and how it would be spent in the state.
"This isn't free money folks. This is borrowed money," Palin said Thursday night in Evansville.
"It looks to us that once again she is putting her national political ambitions ahead of the needs of Alaskans and the responsibilities of her job as our governor," Alaska Democratic Party chairwoman Patti Higgins told reporters Monday in Anchorage.
And even some Republicans took issue with her travels.
"We're a small state. When you get down to the last days of the legislative session it's a little bit like the last two minutes of a basketball game," said Alaska Rep. Jay Ramras, a Republican lawmaker who has clashed with Palin. "You want to have your best players there."
Last week, Palin responded to that criticism by saying it was a quick trip.
"I told lawmakers, you know what, 'Please, don't make me feel that I have to ask your permission, lawmakers, to leave the capital city,'" Palin told reporters.
ABC News' Teddy Davis contributed to this report.