Tucked deep in the thousand-plus pages of the multitrillion-dollar budget bill making its way through the Republican-controlled House of Representatives is a paragraph curtailing a court’s greatest tool for forcing the government to obey its rulings: the power to enforce contempt findings.

It’s unclear whether the bill can pass the House in its current form — it failed in a committee vote Friday and is set to face another test late Sunday evening — whether the U.S. Senate would preserve the contempt provision or whether courts would uphold it.

The fact that GOP lawmakers are including it, however, shows how much those in power in the nation’s capital are thinking about the consequences of defying judges as the battle between the Trump administration and the courts escalates.

The most intense skirmishes to date have come in the lower courts.

One federal judge has found that members of the administration may be liable for contempt after ignoring his order to turn around planes deporting people under the Alien Enemies Act of 1798. Mr. Trump’s administration has scoffed at another judge’s ruling that it “facilitate” the return of a man wrongly deported to El Salvador, even though the Supreme Court upheld that decision.

In other cases, the administration has removed immigrants against court orders or had judges find that the administration is not complying with their directives. Mr. Trump’s deputy director of the FBI, Dan Bongino, called on the president to “ignore” a judge’s order in one of his final appearances on his talk radio show in February.

“Who’s going to arrest him? The marshals?” Mr. Bongino asked, naming the agency that enforces federal judges’ criminal contempt orders. “You guys know who the U.S. Marshals work for? Department of Justice.”

The rhetoric obscures the fact that the administration has complied with the vast majority of court rulings against it, many of them related to Trump’s executive orders. Mr. Trump has said multiple times he will comply with orders, even as he attacks by name judges who rule against him.

The head of Article III Project, Mike Davis, which pushes for pro-Trump judicial appointments, predicted that Mr. Trump will prevail over what he sees as hostile judges.

“The more they do this, the more it’s going to anger the American people, and the chief justice is going to follow the politics on this like he always does,” Mr. Davis said.

Courts can hold parties to civil litigation or criminal cases in contempt for disobeying their orders. The penalty can take the form of fines or other civil punishments, or even prosecution and jail time, if pursued criminally.

The provision in the Republican budget bill would prohibit courts from enforcing contempt citations for violations of injunctions or temporary restraining orders — the two main types of rulings used to rein in the Trump administration — unless the plaintiffs have paid a bond. That rarely happens when someone sues the government.

Legal experts are gaming out whether judges could appoint independent prosecutors or be forced to rely on Trump’s Department of Justice. Then there’s the question of whether U.S. marshals would arrest anyone convicted of the offense.

“If you get to the point of asking the marshals to arrest a contemnor, it’s truly uncharted territory,” Mr. Noll said.