Judge Alito was approved by the Republican dominated Senate Judiciary Committee 10-to-eight on party lines.
Democrats united in opposition against 55-year-old conservative, saying they fear Judge Alito, if he joins forces with other conservatives on the US high court, will undo years of liberal court rulings.
On Monday, Mr Bush praised Judge Alito as "a very, very smart, capable man" and urged lawmakers to quickly hold a full vote on his candidate.
"He's extraordinarily capable to serve on the Supreme Court," Mr Bush said.
Praise for Alito
The Judiciary Committee chairman, moderate Republican Senator Arlen Specter, also offered unstinting praise of Mr Alito.
"His personal background is exemplary. His professional qualifications are outstanding. His educational achievements are of the highest order," Senator Specter said, announcing that he would vote in favor of the nominee when it goes to the Senate for approval.
The full Senate vote is the final hurdle in the arduous process of becoming a high court justice, one of the most powerful positions in the United States, and comes three months after Bush named him to the post.
But Democrats have closed ranks in opposition to the federal appeals court judge. Most of their reservations have centered on the controversial issue of limits on presidential authority, a topic that has consumed Washington since revelations last month that the administration launched a domestic espionage program following the September 11, 2001 attacks.
Some legal scholars have challenged the Bush administration over its domestic eavesdropping, saying it oversteps constitutional bounds because the program was put in place without court or congressional approval.
During dogged grilling, however, Judge Alito refused to be drawn into the controversy but made some statements that seemed to side with the administration, leaving Democrats to fear the worst.
"This nomination raises the fundamental question of whether the Senate will serve its constitutional role as a check on the president by preserving the Supreme Court as a constitutional check on the expansion of presidential power," said Senator Patrick Leahy, the top Democrat on the Judiciary Committee.
"The president is in the midst of a radical realignment of powers of the government and its intrusiveness into the private lives of Americans, and I believe this nomination is part of that plan," Senator Leahy said.
"This is a nomination that I fear threatens the fundamental rights and liberties of all Americans now and in generations to come," he said.
Democrats critical
Democrats also condemned Judge Alito as a right-wing partisan intent on undoing decades of civil rights gains for women, minorities and the poor.
And they have said they are particularly dismayed that he has been tapped to replace retiring Justice Sandra Day O'Connor, the first woman to serve on the high court, who has consistently voted to uphold the right of American women to choose an abortion.
Judge Alito, a 15-year veteran federal appeals court judge, has left a long paper trail over the years which suggest decidedly anti-abortion views including memos written while working as an attorney in the Ronald Reagan administration, in which he proposed strategies for overturning the Supreme Court landmark 1973 Roe v Wade abortion rights decision.