The White House is lobbying some of the president's most vocal foes, including Senator Ted Cruz, R-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.
Wednesday, the Senate Judiciary Committee will begin hearings on his nomination to the US 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 Srinivasan or risk forcing a change to Senate rules that could prevent Republicans from filibustering nominees.
Beyond its import for other nominations, Srinivasan's confirmation also matters for its own sake. Obama has yet to fill any of the four openings on the appeals court in Washington, which hears many major federal cases and has often been a steppingstone for future Supreme Court justices. Four of the current justices served there first.
As a 46-year-old lawyer with bipartisan backing who would become the first appeals court judge of South Asian heritage, Srinivasan himself is a potential Supreme Court candidate.
"There really is no good reason not to confirm Sri - and no good reason after his hearing not to give him a speedy vote," said Walter E. Dellinger III, who served as acting solicitor general under President Bill Clinton and is one of the organizers of the effort to burnish Srinivasan's centrist credentials so Republicans will feel they have little choice but to support him.
Speaking of his efforts to line up conservatives on Srinivasan's behalf, Dellinger added, "It was not a hard sell."
Like some recent Supreme Court nominees, Srinivasan, the principal deputy solicitor general, does not have the kind of long paper trail on divisive issues that could complicate his prospects, although that background also creates anxiety among some ofthe president's allies.
He was a point guard on his high school basketball team in Kansas where his teammate was Danny Manning, the star University of Kansas player who went on to play professionally. In Washington, he has played an occasional game with Cruz.
He has argued two dozen cases before the Supreme Court. Most recently, he was on the Obama administration's side in arguments last month over the constitutionality of the Defense of Marriage Act.When he appears before the justices, he is one of the few lawyers to speak completely without notes.
He was also a clerk to Justice Sandra Day O'Connor, a Reagan appointee, and has taken on causes that are not conventionally liberal. Several years ago, he represented imprisoned former Enron executive Jeffrey K. Skilling, winning a decision that significantly limited the federal law used to prosecute corrupt politicians and public figures.
Senate Republicans are largely withholding public judgment on Srinivasan's nomination until after his hearing.
The list of high-profile lawyers supporting his nomination reads like a strange bedfellows guide to Washington.
Along with Starr, Paul D. Clement and Theodore B. Olson, both solicitors general under George W. Bush, signed Dellinger's letter. So did Seth P. Waxman, a Clinton appointee, and Neal Katyal, Srinivasan's predecessor as principal deputy solicitor general who represented the Obama administration from 2009 to 2011.
The efforts to push Srinivasan to confirmation - some directed by the White House, and others led by coalitions of lawyers that have the Obama administration's blessing - would probably not have been necessary in years past. Democrats started aggressively filibustering judicial nominees during the George W. Bush administration, a practice Republicans have escalated.
"We've lived through this atmosphere since the confirmation hearings of Judge Bork," Starr said, recalling the bitter 1987 defeat of Robert H. Bork, a conservative Supreme Court nominee, by Democrats.
"I wish," Starr added, "we could get past the era of such a deeply politicized process."
In part because the Obama administration has been slow to name appellate judges when vacancies occur and in part because of Republican efforts to deny nominees votes in the Senate, no new judge has joined the District of Columbia court to which Srinivasan has been nominated since Bush was president.
Obama's only other nominee to the court, Caitlin J. Halligan, was named to fill the vacancy created by the elevation of John G. Roberts Jr. to the Supreme Court. Republicans last month for a second time prevented the Senate from voting on Halligan, and she then asked that her nomination be withdrawn.
Of the judges who hear full case loads, four were appointed by Republican presidents and three by Clinton.
The court is of major importance to any White House because it often takes cases that decide the constitutionality of rules and regulations issued by federal agencies. Some recent decisions, like one this year stating the president had violated the Constitution when he installed three officials on the National Labor Relations Board while the Senate was in recess, have dismayed the Obama administration.
Since Halligan withdrew, the White House and Srinivasan's allies have rallied to his defense. In addition to Dellinger's letter, a group of more than two dozen former Supreme Court clerks who worked for justices as ideologically far apart as Clarence Thomas and John Paul Stevens drafted their own letter.
Last week, the White House press secretary, Jay Carney, opened one of his daily media briefings with a plea for the Senate to confirm Srinivasan and to stop what he called a continuous and arbitrary pattern of delay with judicial nominees.
Senate Democrats have discussed with the White House the possibility of putting nominees forward for all four of the vacancies on the Washington court at once. And on Tuesday Sen. Harry Reid, D-Nev., the majority leader, said he expected the White House to move forward soon with more nominations.
"We expect in the next couple of weeks - I spoke to the White House this morning - three more nominations," he said.
Reid decided earlier this year not to make major changes to rules governing the filibuster, but he has become increasingly exasperated by a series of drawn-out nomination fights.
He hinted this past weekend that unless Republicans started approving more of the president's judicial nominees, he would resort to a procedural maneuver that would allow him to limit Republicans' ability to prevent votes on nominees.
On Tuesday, Sen. Mitch McConnell, the Republican leader, appeared sensitive to that possibility, saying, "We treated this president quite fairly."