Sen. Rand Paul's (R-Ky.) filibuster, which raised constitutional, due-process concerns about the use of drones against Americans, drew criticism from Sens. John McCain (R-Ariz.) and Lindsey Graham (R-S.C.).
Bush said that despite the high-profile debate, the GOP was still in sync over a broad range of issues.
"It is OK to have a disagreement. We don't march lockstep 100 percent in agreement all the time, but on these broader issues I think there is broad support and that's what is emerging in the Republican party going forward," he said on the program "State of the Union."
Paul held the floor for nearly 13 hours, delaying the Senate confirmation of John Brennan to run the Central Intelligence Agency. Brennan was later confirmed.
Paul had asked the White House to clarify that the president did not have the authority to use armed drones to target Americans on U.S. soil.
Attorney General Eric Holder later sent a letter to Paul saying that the president would not use drone strikes against citizens who are not engaged in hostile activity.
Sens. McCain and Graham had strongly criticized Paul’s filibuster, saying it raised “ridiculous” arguments and “cheapened” the debate over drone policy.