The battle over President-elect Donald J. Trump’s cabinet choices will escalate this week with Senate confirmation hearings set for more than a dozen prospective nominees, who will face a barrage of questions from Democrats hoping to enlist Republicans in knocking at least a few out of contention.

The most high-profile and potentially contentious hearing is scheduled for Tuesday, when the Senate Armed Services Committee is scheduled to consider the expected nomination of Pete Hegseth, the former Fox News personality and combat veteran, for secretary of defense. Senate committees have also set public reviews for the choice for attorney general and those tapped to run the State, Treasury, Homeland Security, Energy, Interior, Transportation and Veterans Affairs Departments and the C.I.A., among others.

Despite criticism of the backgrounds and experience of some of his picks, Mr. Trump has urged Senate Republicans to stay united and quickly deliver the team he has selected in the opening days of the administration. How the G.O.P. responds will provide an early test in the relationship.

Mr. Trump and his Republican allies in the Senate would like to be have at least some officials in place within hours of his swearing-in next Monday, but while top Republicans say they are committed to rapidly advancing his picks, the chances of more than a few being ready for votes on Inauguration Day are low.

“The president ought to have his team in place early, especially his national security team,” Senator John Barrasso of Wyoming, the No. 2 Senate Republican, said on Sunday. “If Democrats try to drag out the process, the Republican Conference is ready to work around the clock, including weekends and nights, to get them in place.”

Mr. Hegseth has faced intense scrutiny because of accusations of sexual misconduct and excessive drinking, as well as his acknowledgment of reaching a financial settlement with a woman who accused him of sexual assault at a conservative convention in 2017. He has also faced criticism for comments about limiting the role of women in the military and will be pressed about his handling of two veterans advocacy groups that ran into financial trouble.

“Your past behavior and rhetoric indicates your inability to effectively lead this organization and properly support our service members,” Senator Elizabeth Warren, a Massachusetts Democrat who sits on the committee, wrote to Mr. Hegseth last week in a 33-page letter with more than 70 questions for Mr. Hegseth.

After some initial unease, Senate Republicans have become more confident about Mr. Hegseth’s chances for confirmation as he has made personal visits to Senate offices to address Republican concerns.

“As people hear him, I think they will gain more confidence in his abilities,” said Senator Mike Rounds, Republican of South Dakota.

But Democrats on the panel are already raising alarm that they have not been able to view an F.B.I. background check on Mr. Hegseth — information that so far has been shared only with the panel’s chairman and senior Democrat — and may not receive complete information about his past.

Though confirmation hearings can produce drama, it is rare for nominees to be defeated on the floor. Just one has been rejected in the last 36 years, when John Tower, a former Republican senator from Texas, fell short of the votes for secretary of defense in the administration of President George H.W. Bush. Senators traditionally tend to give presidents deference in their top administration choices, and those who run into trouble typically withdraw before a vote.

Democrats intend to use the hearings to press the nominees on how they will follow through on G.O.P. campaign pledges to help the working class while showcasing serious issues with the candidates in hopes of chipping away at Republican support.

“We want to show who they really are,” Senator Chuck Schumer, Democrat of New York and the minority leader, said in an interview. “Some of them carry a lot of baggage.”

While past presidents were able to get at least some cabinet members on board on Day 1, Democratic resistance and the Senate’s byzantine rules will make winning immediate confirmation of members of Mr. Trump’s team very difficult. Changes in confirmation procedures and intensifying partisanship over nominees have significantly diminished chances for first-day approval even of those in the national security realm.

For instance, President Barack Obama saw six cabinet nominees confirmed on Jan. 20, 2009, while Robert M. Gates was carried over as secretary of defense. A handful of others, including Hillary Clinton as secretary of state, were confirmed within a few days. At that time, nominees were theoretically subject to a 60-vote threshold, forcing Mr. Obama and his predecessors to make selections more able to clear that hurdle.

In 2013, Democrats changed Senate rules so that nominees for administration slots and judicial seats could be confirmed on a straight majority vote with no threat of a 60-vote requirement, allowing presidents to name candidates who could prevail on party-line votes but increasing the chances for partisan division.

In 2021, Mr. Trump was able to win two cabinet confirmations on Jan. 20, filling the top defense and homeland security posts, as Democrats cooperated in filling key national security slots for the new administration with military generals boasting significant experience.

President Biden was able to win the confirmation of just one top official on Jan. 20, 2021, when Avril D. Haines was approved as director of national intelligence. Secretary of Defense Lloyd J Austin III was confirmed two days later and Secretary of State Antony J. Blinken on Jan. 26. Democrats say the nominee they are most inclined to clear the way for this year is Senator Marco Rubio, their Republican colleague from Florida, for secretary of state.

Part of the issue is that nominations cannot become official until the president takes office, meaning Mr. Trump can submit formal paperwork only after he is sworn in. The Senate is allowed to hold hearings, but clearing prospective nominees for the floor requires some Democratic cooperation.

Democrats would be highly unlikely to provide much help for nominees such as Mr. Hegseth. Republicans would then have to hold committee votes and follow floor procedures that will consume time, as well. Hearings for other contentious nominees such as Robert F. Kennedy Jr. for health secretary and Tulsi Gabbard for intelligence director are pending.

In the run-up to the hearings, Democrats and some Republicans have objected to proceeding because not all the traditional ethics and financial paperwork has been available. They have also pressed for access to F.B.I. background reports. Republicans have said that they expect most of the requirements to be met before any votes and that they intend to fulfill their duty of providing advice and consent.

“I think there is a real desire to move these through as quickly as possible,” Mr. Rounds said. “But we are going to do our job, too.”