The White House has asked conservative groups to "calm people down" and supporters say critics should give President Bush a little space as he considers nominees to replace retiring Supreme Court Justice Sandra Day O'Connor (search), Republican sources told FOX News on Tuesday.

"What's really important is for everybody to take a deep breath, and take 10 steps back and let the president go through this process," said Brad Blakeman, a former deputy assistant to the president.

Other backers say the president does not have a litmus test for his nominee and neither should conservatives.

"If they're going to start on Alberto Gonzales (search) because he may be pro-choice, think of what the left side is going to do if he comes in with a justice who might appear, or they think is leaning to the pro-life side," said former U.S. Sen. Al D'Amato of New York.

In an interview before leaving for Europe, Bush bristled at grumbling among conservatives who argue that Attorney General Gonzales would not be a suitable nominee for the high court.

"Al Gonzales is a great friend of mine. I'm the kind of person, when a friend gets attacked, I don't like it. We're lucky to have him as the attorney general and I'm lucky to have him as a friend," the president told USA Today.

Blakeman said pressure won't work on this president in any case.

"This president will not be bullied, he will not be threatened," he said.

Whomever the president picks as a nominee, the timing of the announcement of his pick will be key. Bush made clear on Friday, the day O'Connor's retirement was announced, that he wants to see a new justice in place when the court begins its new term in October.

The White House said Tuesday that the selection process will take some time. Once the president names a nominee, the FBI (search) will need to complete its background investigation, which could take four to five weeks. The Senate will then hold hearings and likely provide questionnaires for the candidate to answer.

Because Congress is in recess during the month of August, some strategists say the president doesn't need to hurry since nominating someone too far in advance would simply give critics more time to attack the president's choice.

"The problem would be the potential Bork problem, where opponents of the nominee would be able to characterize the nominee disadvantageously during that time," said Sen. John Cornyn, R-Texas, a former Texas state Supreme Court justice, referring to failed Reagan Supreme Court nominee Robert Bork.

"Sort of like a pinata that everybody can take a whack at who happens to want to try to tear that nominee down," Cornyn said.

But with members of Congress on vacation and making official visits overseas, some court watchers say an August nomination could prevent some of the more intense attacks on the candidate.

"If you sort of follow the way public policy issues are debated in Washington, often the sharpness of the debate is less when Congress is not in session and the town is on vacation," said Ben Ginsberg, head of Progress for America. "It's a little bit harder to compile the opposition in one place."

Blakeman said the president wants the shortest period of time between the announcement and hearing to prevent too much "mischief" or "too much opportunity for people to get bitter and for it to degenerate."

However, just because the Senate is on recess, Cornyn said it is still "within the realm of possibility" that the Judiciary Committee could hold a hearing in August.

Click in the box near the top of the story to watch a report by FOX News' Jim Angle.