President Bush upgraded Roberts' nomination to the top position on the high court after the conservative chief justice succumbed to thyroid cancer at his home in Arlington, Va. on Saturday.
Federal appellate Judge Roberts was originally slated to fill the seat of Associate Justice Sandra Day O'Connor, who earlier this year announced her plans to retire once her replacement is confirmed.
President Bush has urged the Senate to confirm Roberts by the Oct. 3 start of the court's new term.
"The passing of Chief Justice William Rehnquist leaves the center chair empty, just four weeks left before the Supreme Court reconvenes," the president said Monday. "It's in the interest of the court and the country to have a chief justice on the bench on the first full day of the fall term."
If a replacement is not confirmed, the court's oldest member, 85-year-old liberal Justice John Paul Stevens, will be in charge. Stevens filled in for Rehnquist when the chief justice was absent from the bench for several months after announcing his cancer diagnosis last October.
Some Democrats, including Sen. Edward Kennedy, Mass., called for a longer delay after President Bush recast Roberts' nomination. "Before the Senate acts on John Roberts' new nomination, we should know even more about his record, and we should know whom the president intends to propose to nominate as a replacement for Sandra Day O'Connor," Kennedy said, according to Reuters.
Previously negotiated rules governing the Senate hearings, which will start Monday at noon with opening statements from each senator on the panel, will remain in place, said Specter.
Roberts will face questioning beginning Sept. 13, with the 10 Republicans and eight Democrats on the committee examining him in order of their seniority, reported the New York Times.
"It is our expectation that we will be able to complete the hearings that week," Specter said.
The full Senate may vote on Roberts' nomination in late September.
Elsewhere in Washington, Rehnquist's casket was carried up the steps of the Supreme Court on Tuesday by former clerks, including Roberts.
Lining the stairs were six justices, including O'Connor, who was in tears as the casket passed. Absent were Justices Anthony Kennedy and David Souter.
Roberts and seven other pallbearers brought the flag-draped casket to the Great Hall, where busts of past chief justices are displayed in niches and on marble pedestals along the walls, according to the Associated Press.
Public viewing was to take place on Tuesday and Wednesday. Funeral services for friends and family will be held at St. Matthew's Cathedral in Washington, and the burial at Arlington National Cemetery will be private.