Mr Bush said yesterday he was confident that John G Roberts would get "a timely hearing, a fair hearing" from the US Senate.
Abortion, a polarising issue for Congress, will be to the forefront in the confirmation battle, conceded Fred Thompson, the former senator who will shepherd Judge Roberts through the Senate. But Mr Thompson cautioned lawmakers not to read too much into the judge's seemingly conflicting legal positions on Roe v Wade, the 1973 Supreme Court decision legalising abortion.
"Many of the positions he's taken are positions he took as an advocate ... representing a client," said Mr Thompson.
Democratic concern over Roberts's abortion views stem from two seemingly contradictory positions he took on Roe v Wade.
In a brief that he filed with the Supreme Court while serving as deputy solicitor general in the administration of the first President Bush, Roberts said that Roe v Wade "was wrongly decided and should be overruled". But he told senators during his 2003 confirmation hearings for his current post that the decision was "the settled law of the land".
Mr Bush introduced the 50-year-old federal appeals court judge to the American nation on Tuesday night, calling him a man with "a good heart" and a jurist who will "strictly apply the constitution in laws not legislate from the bench".
Judge Roberts met yesterday with leaders in the Senate, which will decide if he will replace retiring Justice Sandra Day O'Connor and become the first new Supreme Court member in more than a decade.
Reaction from Republican senators was overwhelmingly supportive.
Majority Leader Bill Frist of Tennessee called for confirmation proceedings that "treat Judge Roberts with dignity and respect" and lead to a yes or no vote before the court's term begins on October 3.
Democrats reacted more cautiously, but there were no instant predictions of a filibuster.
Dianne Feinstein, the only woman on the Senate Judiciary Committee that will hold hearings on the nomination, said the new justice will be critical to the balance of the court, especially in cases involving congressional authority, a woman's right to privacy and environmental protections.
Conservative interest groups were elated, saying the president kept a campaign promise to nominate someone akin to conservative Justices Clarence Thomas and Antonin Scalia.
Liberal groups expressed concerns about Judge Roberts's views on abortion, religious freedom, environmental protections and the First Amendment.
It's unclear how contentious this confirmation battle will be.
Tony Perkins, of the conservative Family Research Council, said there was no doubt there would be a battle for the post. He added that a Roberts appointment would bring a "philosophical shift" to the court, which, he said, had been "shifting to the left" over the past 40 years.