The fate of President Bush's nominee could hinge on how he justifies domestic eavesdropping programs that some lawmakers contend are illegal and started without congressional approval.
The Senate Intelligence Committee begins confirmation hearings Thursday.
"There's no question that his confirmation is going to depend upon the answers he gives regarding activities of NSA," one committee member, Sen. Chuck Hagel, R-Neb., said on ABC's "This Week."
"If he comes up to the appropriate committee, the Intelligence Committee and does not respond, then it will make it very, very difficult," fellow committee member Joe Biden, D-Del., said.
Asked on CBS' Face The Nation if Hayden's nomination to succeed Porter Goss was in trouble, Sen. Arlen Specter, R-Pa., said, "I would say that there are a lot of questions which General Hayden has to answer. He's a first-class professional, but he has been in charge of a program where we need a lot more information."
Specter, chairman of the Senate Judiciary Committee, does not serve on the Intelligence Committee, but he wants to ask representatives of telephone companies that cooperated with the NSA to testify before his panel.
Hagel, who met with Hayden on Friday, has expressed "absolute confidence" in the general and said the hearings should provide the facts on the monitoring programs.
"The American people need to be assured that their government is, in fact, following the law, not just protecting the security interests of our country, but also the constitutional rights of individual Americans," Hagel said. "We can do both. We always have done both."
In his weekly radio address Saturday, Mr. Bush sought to separate the debate about the NSA program from the upcoming confirmation hearings.
But senators are indicating that they will not let that happen. Sen. Patrick Leahy, D-Vt., said on CNN's "Late Edition" that he wants to know from Hayden "how does he justify the illegal spying upon millions of millions of ordinary Americans?"
Mr. Bush is trying to push Hayden's qualifications to the top of the debate, noting that the general, who was formerly the head of the NSA, was unanimously confirmed last year for his current post as deputy national intelligence director.
The president called his choice "supremely qualified" to be the CIA's next chief. He ticked off Hayden's involvement in recent reforms of the U.S. intelligence community and his experience as a former Pentagon and White House official and in the Bulgarian embassy during the Cold War.
"Mike knows our intelligence community from the ground up," Mr. Bush said.
Lawmakers have been pressing the Bush administration for information about the NSA's database of telephone records since its existence was made public on Thursday.
Some Republicans, including Senate Armed Services Chairman John Warner of Virginia, have said that Hayden should not bear the burden for the spying because he relied on the advice of top government lawyers when the programs began.
But Sen. Ron Wyden, D-Ore., an Intelligence Committee member, said he now questions Hayden's credibility. "The American people have got to know that when the person who heads the CIA makes a statement that they are getting the full picture," Wyden said.