WASHINGTON — The debate about whether to continue the dragnet surveillance of Americans’ phone records is highlighting divisions within the Democratic and Republican parties that could transform the politics of national security.

While some leading Democrats have been reluctant to condemn the National Security Agency’s tactics, the GOP has begun to embrace a libertarian shift opposing the spy agency’s broad surveillance powers — a striking departure from the aggressive national security policies that have defined the Republican Party for generations.

The lines are drawn but not in the traditional way. The Republican National Committee, civil libertarians like Kentucky Sen. Rand Paul and liberals like Massachusetts Sen. Elizabeth Warren are on one side of the debate. Florida Republican Sen. Marco Rubio, Democratic former Secretary of State Hillary Rodham Clinton and the House and Senate leadership are on the other side, defending the Obama administration’s surveillance programs as necessary to prevent terrorism.

The split in each party could have practical and political consequences ahead of the 2014 midterm elections and the 2016 presidential contest.