"This post has happened to me quickly and I do think it is a very awesome responsibility [President Obama] has and we in the Senate have to do this thing right," Sessions said. He added that he does not have a personal favorite among the prospective candidates.
Sessions stressed that an appointment to the Supreme Court can last a lifetime. "Once this confirmation occurs, then they are no longer accountable to the American people really," he said.
Schieffer asked the Republican if he was bothered by President Obama's use of the word "empathy" in describing his ideal candidate. Critics have argued that by saying he wants someone with empathy the president is implying that his nominee will push an agenda.
Sessions said Obama's word choice was "troubling," adding: "What does empathy mean? You like one party or another party that is appearing before you and you are going to doctor your opinion to favor the one that you like?"
He added that he is not sure if the president's word choice is being misconstrued.
Watch the interview here:
In the interview, Sessions noted that President Obama "comes from an activist judicial background" and said that those involved in the confirmation "need to look at [his] nominee carefully."
The senator said that the president has acknowledged his concerns and "indicated that we may not agree totally but we may be closer to one another than we think."
Along with three other Senate leaders, Sessions met with the president earlier this week to discuss potential picks. The senator confirmed that "no names" were mentioned in the meeting and that the president hopes to produce a nominee "as soon as he could."
"I think he needs to be careful and not make a mistake," Sessions said about the president's looming decision.
"He did indicate that some of the names that are out there are under consideration," Sessions added.
The senator told Schieffer that a unifying nominee could be out there. "The problem is [Mr. Obama] has a lot of supporters who want an activist type nominee...and he has some inclinations, I think, clearly in that direction."
He reiterated that a homosexual nominee would have a fair shot at the post. "How a person conducts themselves over a period of time does have an impact," he added.