Lawyers for President Trump in line to take top jobs at the Justice Department sparred with Democrats on Wednesday over whether the administration could simply ignore some court orders — an early skirmish in a larger fight over the White House’s efforts to claim more sweeping presidential powers.

The debate, before the Senate Judiciary Committee, unfolded as three nominees testified during a confirmation hearing to join the upper ranks of the Justice Department. Two of the nominees, Harmeet K. Dhillon and D. John Sauer, have long worked as personal lawyers for Mr. Trump.

The third, Aaron Reitz, selected to lead the Office of Legal Policy, was questioned about an old social media post in which he suggested that Mr. Trump follow the example set by President Andrew Jackson, who ignored a Supreme Court order in 1832.

“There is no hard and fast rule about whether, in every instance a public official is bound by a court decision,” he said Wednesday. “There are some instances in which he or she may be lawfully bound and some instances where he or she may not be lawfully bound.”

Mr. Sauer, who has represented Mr. Trump before the Supreme Court and is the solicitor general nominee, was pressed on the same point. He replied, “It’s hard to make a very blanket, sweeping statement about something without being presented with the facts and the law.”

The back-and-forth came as dozens of legal challenges have been mounted against the Trump administration on several issues, many of them revolving around the president’s efforts to fire thousands of federal employees as he seeks to overhaul the government. Democrats have questioned whether Mr. Trump might simply ignore rulings against his favor.