WASHINGTON — With a coordination and an energy that echo a Supreme Court nomination fight, the Obama administration is pushing for the confirmation of a senior Justice Department lawyer to the country’s most prestigious appellate court. If the effort fails, it could lead to a confrontation with the Senate over the long-simmering issue of judicial nominees.

The White House is lobbying some of the president’s most vocal foes, including Senator Ted Cruz of Texas. Administration officials are trumpeting the endorsement of top Republican lawyers like Kenneth W. Starr, the special prosecutor who investigated the Clintons. And former clerks for Supreme Court justices, liberal and conservative, are writing letters of support for the nominee, Sri Srinivasan.

On Wednesday, the Senate Judiciary Committee will begin hearings on his nomination to the United States Court of Appeals for the District of Columbia Circuit. The nomination will test an aggressive new strategy that the White House and Democrats are hoping will put Republicans in a bind: approve the highly regarded Mr. Srinivasan or risk forcing a change to Senate rules that could prevent Republicans from filibustering nominees.

Beyond its import for other nominations, Mr. Srinivasan’s confirmation matters for its own sake. Mr. Obama has yet to leave his mark and fill any of the four vacant seats on the court, which often decides major federal cases and has been a steppingstone for Supreme Court justices. Four of the current justices served there first.