Joined by Roberts outside the White House after a private breakfast meeting, Mr. Bush told reporters, "We will push the process forward." He said both he and Roberts believe he should be sworn before the new court term begins in October.
Roberts then headed to Capitol Hill for meetings with leaders in the Senate, which will decide whether he will replace Sandra Day O'Connor and thus become the first new Supreme Court member in more than a decade.
Former Sen. Fred Thompson of Tennessee, who will help Roberts through the grueling confirmation process, told CBS News' The Early Show that Roberts is "one of the most qualified nominees in the history of Supreme Court nominees and in the history of our country."
Thompson said the president and his staff have talked to "over 70 senators and seriously considered the comments that they had and suggestions that they made. We'll continue that today."
Reaction from Republicans 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 Oct 3.
Democrats reacted more cautiously, but there were no instant predictions of a filibuster.
"The president has chosen someone with suitable legal credentials, but that is not the end of our inquiry," Senate Democratic leader Harry Reid, D-Nev., said.
Sen. Dianne Feinstein, D-Calif., 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 when it rules on cases involving congressional authority, a woman's right to privacy and environmental protections.
"I will keep my powder dry until the due diligence is completed," Feinstein said.
Roberts' Republican credentials are well established, reports CBS News Correspondent Joie Chen He was an assistant legal counsel for President Reagan, deputy solicitor general in President George H.W. Bush's administration, and was appointed to the D.C. Appeals Court by the current president just two years ago.
President Bush also liked Roberts' personal story. Born in Buffalo, he worked in a steel mill to pay his way through Harvard, was a top graduate of Harvard Law, then served as current Chief Justice William Rehnquist's law clerk.
During his legal career, he argued 39 cases before the Supreme Court.
"I always got a lump in my throat whenever I walk up those marble steps to argue a case before the court, and I don't think it was just from nerves," Roberts said at the White House Tuesday night.
He will now have to steel his nerves for what could become a tough confirmation fight.