Bush's nomination of General Michael Hayden has provoked some concern over an active-duty military officer heading the civilian CIA.
There have also been questions raised after a USA Today report this week said the National Security Agency, NSA, was amassing data on tens of millions of domestic telephone calls in the US in an effort to uncover terrorist activities.
Hayden was head of the NSA between 1999 and 2005, a time when the database would have been compiled.
Bush, however, praised his choice in his weekly radio address on Saturday.
"In Mike Hayden, the men and women of the CIA will have a strong leader who will support them as they work to disrupt terrorist attacks, penetrate closed societies, and gain information that is vital to protecting our nation," he said.
"I urge the Senate to confirm him promptly as the next director of the CIA."
Hayden, an Air Force general, was picked to replace Porter Goss, who resigned under pressure last week.
Bush has come under fire following the USA Today report but clims that he is not "trolling through" Americans' personal lives.
However, a poll for the Newsweek magazine on Saturday showed that 53% of Americans polled believe that the reported NSA database of phone records goes too far in invading people's privacy.
But 41% saw the massive phone database as necessary to combat terrorism.
"In light of this news and other actions by the Bush-Cheney administration, 57% of Americans say they have gone too far in expanding presidential power, while only 38% say they have not," the magazine said.
Just 35% of those polled said they approved of the way the president is handling his job, which is down one percent since the last Newsweek poll.
Asked how history would view Bush, 50% of those polled said he will be viewed as a below average president.
Bush is closing in on the unpopularity level of Richard Nixon, a former president, (24%) at the moment of his resignation in 1974 over the Watergate scandal.