Snow, speaking on "FOX News Sunday," said that if the amendments receive a full airing over a couple of days of debate, "we're going to get a better bill, and it's going to be one that answers the expressed objections of a lot of people."
Snow said border security, amnesty, holding employers accountable and raising the requirements of citizenship are key issues to be discussed.
Snow also said a Senate vote of no confidence regarding Attorney General Alberto Gonzales would be a "purely symbolic vote" that would have no effect on President George Bush. He said it's a combination of a Senate unable to deliver on its promises and attempts by some to find a political advantage.
Asked about the president's decision not to renominate Gen. Peter Pace as chairman of the Joint Chiefs of Staff hasn't weakened him politically.
"The American people issued a vote of no confidence in Congress and in the Senate," Snow said. "I don't know if you saw it, but (Senate Majority Leader) Harry Reid's approval rating is 19 percent."
Swim Week Miami Beach 2014 [PHOTOS]