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."