WASHINGTON — Senator Rand Paul’s intention was to highlight his misgivings about how drones are used. He ended up enmeshing his fellow Republicans in a broader debate over national security that scrambled the politics of left and right.

After invoking and being embraced by civil-liberties-minded liberals during a 13-hour filibuster starting Wednesday on the Senate floor, Mr. Paul, of Kentucky, was showered with praise on Thursday by both the Tea Party movement and the provocateurs of the peace group Code Pink. Senator Mitch McConnell of Kentucky, the Republican minority leader, praised Mr. Paul’s conviction.

Mr. Paul, a libertarian in the mold of his father, former Representative Ron Paul, pointedly questioned whether the government had the authority to kill an American citizen in the United States with a drone strike — an effort that generated a tremendous following on social media.

But he was assailed by two of his party’s most prominent national security hawks, Senators John McCain of Arizona and Lindsey Graham of South Carolina. They took to the floor on Thursday to defend President Obama’s aggressive use of drones against Al Qaeda and its affiliates and to suggest that Mr. Paul and his backers had engaged in scaremongering.