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WASHINGTON – For President Obama, the first test of his second term will come quickly this week when Chuck Hagel and John Kerry, his nominees for the two biggest national-security posts, take critical steps toward winning Senate confirmation. They are likely to get very different receptions.

Senator Kerry, the Massachusetts Democrat whom Mr. Obama selected to succeed Hillary Rodham Clinton as secretary of state, is expected to breeze through his hearing on Thursday before the Senate Foreign Relations Committee, which he still leads.

Mr. Hagel, the president's nominee to succeed Defense Secretary Leon E. Panetta, has begun the uphill task of winning over hostile Republicans. The Senate Armed Services Committee has set Jan. 31 for Mr. Hagel's hearing, but in one of the most important steps of that campaign, he is scheduled to meet this week with a vocal skeptic and former close friend, Senator John McCain of Arizona.

But while Mr. McCain continues to express misgivings about Mr. Hagel's positions on the Iraq war and Iran, officials note he has not declared he would vote against Mr. Hagel, a Republican former senator from Nebraska who, like Mr. McCain, is a Vietnam veteran.

White House officials say they are increasingly sanguine about Mr. Hagel's chances to win confirmation. Democratic senators have fallen into line since he won the blessing of Senator Charles E. Schumer of New York, the most influential Jewish member of the Senate. The endorsement was viewed as crucial by the White House because it allayed concerns among Democrats about Mr. Hagel's positions on Israel and his use of the phrase "Jewish lobby" to refer to pro-Israel lobbying groups.

Privately, administration officials figure that Mr. Hagel could get as many as 60 votes, a threshold that would allow him to overcome a filibuster. Even with a few votes shy of 60, Congressional aides said, it is not clear Republicans will try to block his confirmation.

Minutes after delivering his Inaugural Address on Monday, Mr. Obama signed papers formally nominating Mr. Hagel and Mr. Kerry, as well as two of his other choices for key administration jobs: John O. Brennan for director of the Central Intelligence Agency, and Jacob J. Lew for Treasury secretary. Mr. Lew would succeed Timothy F. Geithner, who announced his resignation this month. Mr. Brennan would succeed David H. Petraeus, who resigned in November after admitting to an extramarital affair.

"I'm sending a few nominations up, which I know will be handled with great dispatch," Mr. Obama said, as Congressional leaders, and a chuckling Vice President Joseph R. Biden Jr., looked on.

But Republicans continue to express doubts about Mr. Hagel's skepticism toward American sanctions on Iran over its nuclear program, as well as about his openness to negotiating with Hezbollah. In recent meetings on Capitol Hill, Mr. Hagel has sounded a more hawkish tone.

"If he has answers for members who have concerns about his past statements," said Senator Susan Collins, Republican of Maine, who met with Mr. Hagel last week, "then I think the chances of his being confirmed will become fairly strong.

"If, on the other hand, he gives answers that appear contradictory or do not demonstrate how his thinking has evolved," the outlook for his confirmation will be less clear, she said.

Aside from his Senate meetings, Mr. Hagel has kept a low profile in recent days. He did not attend the inauguration or show up for Mr. Biden's swearing-in ceremony on Sunday, despite having a seat reserved for him (a logistical mix-up, an official said, since he had decided to stay home to prepare for his confirmation).

As Mr. Hagel's prospects have improved, some analysts say the nominee to watch is Mr. Brennan, the White House counterterrorism adviser Mr. Obama has chosen for the C.I.A.. Immediately after his nomination was announced, Mr. Brennan began encountering resistance from Republicans over alleged national-security leaks after the raid that killed Osama bin Laden.

But now, Mr. Brennan is facing thorny questions from Democrats over the use of drone strikes and the killing of American citizens in counterterrorism operations – decisions in which he was deeply immersed as a White House adviser.

Last week, Senator Ron Wyden of Oregon, a Democrat on the Intelligence Committee, wrote to Mr. Brennan, demanding that lawmakers be allowed to review the Justice Department's legal opinion on assassinations, including that of Anwar al-Awlaki, the American-born cleric who was killed in a drone strike in Yemen in 2011.

The White House has fought to keep these opinions secret. Senator Dianne Feinstein, Democrat of California and the chairwoman of the Intelligence Committee, has also called on the administration to release the legal opinion in the Awlaki case. She is likely to raise it in Mr. Brennan's confirmation hearing, which is scheduled for Feb. 7.

The only nominee who seems likely to have a trouble-free experience is Mr. Kerry. Unlike Mr. Hagel, Mr. Kerry was a visible presence at the Capitol on Monday, shaking hands with Mr. Obama after his speech and chatting later with former President Bill Clinton.

Mr. Kerry's hearing, in fact, may seem anticlimactic, coming the day after Mrs. Clinton's long-awaited Congressional testimony on the deadly attack on the American mission in Benghazi, Libya. On Wednesday morning, she will testify before the Senate Foreign Relations Committee. The hearing will be led by Senator Robert Menendez of New Jersey, the next highest-ranking Democrat on the committee, since Mr. Kerry cannot preside over his own confirmation.

She will testify before the House Foreign Affairs Committee in the afternoon.