Sen. Lindsey Graham, R-S.C., another leader of the opposition to Hagel, referred to a letter he received from Hagel in response to questions about past statements on Israel. Graham said that, as a result, he'll take Hagel "at his word, unless something new comes along."
Still, the weeklong delay buys Hagel's opponents even more time to rally additional opposition.
White House chief of staff Denis McDonough, making his first appearances on the Sunday talk shows in his new role, was asked if the delays in filling out Obama's Cabinet presented a threat to national security.
"It's a grave concern," he said.
Hagel "has one thing in mind: how do we protect the country," McDonough said, adding that there was nothing to worry about in any disclosures about Hagel that may still come.
Graham said senators were taking seriously their responsibility to scrutinize "one of the most unqualified, radical choices for secretary of defense in a very long time."
Last week, Obama criticized Republican senators for delaying the nomination, accusing them of playing politics with national security.
"It's just unfortunate that this kind of politics intrudes at a time when I'm still presiding over a war in Afghanistan and I need a secretary of defense who is coordinating with our allies to make sure that our troops are getting the kind of strategy and mission that they deserve," he said during a Google-sponsored online forum.
McDonough appeared on ABC's "This Week," while McCain spoke on NBC's "Meet the Press" and Graham was interviewed by "Fox News Sunday."