Kentucky GOP Sen. Rand Paul joined Stuart Varney on Thursday's Your World to give his first reaction moments after voting against a landmark immigration bill that passed in the Senate.

Varney asked Paul what his main objections were to the legislation, and the lawmaker's answer was simple: "I just think immigration reform should be dependent on border security first [before we go forward]" he said.

"I just couldn't go along with it," he said, "and I'm fearful that [...] we'll still have significant illegal immigration with this bill."

As for whether or not the bill could be fixed and then pass in the House, Paul hedged, replying with uncertainty. The problem, he contended, is that the current bill in the Senate gives the president veto power and the authority to make the ultimate decision - one that Paul said should be retained by Congress.