(Image Credit: Bebeto Matthews/AP Photo)

ABC News' Sunlen Miller and Rosalyn Oshmyansky report:

Day two of Susan Rice's charm offensive on Capitol Hill brought little support for the U.N. ambassador to become the next secretary of state if nominated by President Obama.

After meeting privately with Rice this morning, moderate Republican Sen. Susan Collins of Maine said she still had questions about the embassy attack in Libya that "remain troubling" and needed to be answered before she can support Rice for secretary of state.

"I continue to be troubled by the fact that the U.N. ambassador decided to play what was essentially a political role at the height of a contentious presidential election campaign by agreeing to go on the Sunday shows to present the administration's position," Collins said after her meeting with Rice. "I would need to have additional information before I could support her nomination."

By way of comparison, Collins jumped at the opportunity when asked about Sen. John Kerry, D-Mass., whose name is also on the short list said to be considered for the next secretary of state.

"I think John Kerry would be an excellent appointment and would be easily confirmed by his colleagues," Collins said.

As for Rice, Collins brought up the 1998 bombing of the two U.S. embassies in Tanzania and Kenya when Rice was the assistant secretary for African Affairs. The senator said it's troubling that lessons seemed to be missed because so much of what happened in Benghazi "eerily echoes" what happened in the African attacks when Rice was head of the African region for the State Department.

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"In both cases, the ambassador begged for additional security," Collins said, "and those requests, as in the case of Benghazi, were turned down by the State Department."

Collins said today she asked Rice what role she played in turning down requested security at the two embassies in Africa before the 1998 bombings.

"She [Rice] said she would have to refresh her memory but that she was not involved directly in turning down the requests," Collins said, adding, "but, surely, given her position as assistant secretary for African affairs, she had to be aware of the general threat assessment and of the ambassadors repeated request for more security."

Rice has spent the past two days in meetings on Capitol Hill, specifically requested by her with individual senators who have voiced concern about her potential promotion to secretary of state.

After the morning meeting with Collins, Sen. Bob Corker, R-Tenn., had a private meeting with Rice but declined to say afterward whether he would support Rice if the president nominates her. Corker stressed that he hopes Obama will choose someone with independence.

"I would ask the president back step away from all the buzz around this particular situation and take a deep breath and decide who is the best secretary of state for our country," Corker said this afternoon. "Hopefully, it will be someone who shows independence and have the ability to lead this nation and the world."

The senator's careful response stands in direct comparison to comments he made Tuesday in an interview with Foreign Policy magazine in which he said Rice would make a better Democratic National Committee chairwoman than secretary of state, based on what happened in Benghazi and its aftermath.

Corker was more restrained today, saying he'll withhold judgment until someone is nominated and he's able to thoroughly examine that person's credentials in order to make his own determination.

Corker is next in line to the ranking member of the Senate Foreign Relations Committee so will have a prominent role in the nomination process. He said today that he holds the secretary of state at a higher standard than most cabinet members.

"All of us here hold the secretary of state to a very different standard than most cabinet members," Corker said. "Secretary of state is, no doubt, one of those we want someone of independence. We understand they are going to support the administration and all of their efforts, [but] we want someone who's transparent and direct."

Rice Tuesday met with a vocal and tough crowd of Republican senators: Sen. John McCain, R-Ariz., Sen. Lindsey Graham, R- S.C., and Sen. Kelly Ayotte, R-N.H. The three senators said they were more troubled after their meeting with Rice.

Sen. Joe Lieberman, the independent from Connecticut, so far has been the one lone senator to have met with Rice this week and come away with a positive view.

After his meeting Tuesday, Lieberman said he has his questions answered and does not see anything that would disqualify Rice from potentially becoming the next secretary of state, if nominated.