Senate Democrats triggered the “nuclear option” Thursday, using a shortcut to undercut the chamber’s filibuster rules and giving President Obama a clear path to stack the federal judiciary with ideological allies.

In a tense 52-48 vote, Democrats overturned decades of precedent and reduced the number of votes needed to cut off the filibuster of a nominee from 60 to a simple majority — and in the process tinkering with a tool that has made the Senate unique.

Republicans were hinting at retaliation and said the move further poisoned the atmosphere on Capitol Hill.

Senate Majority Leader Harry Reid, Nevada Democrat, said he didn’t fear retaliation. He said he reached a tipping point after Republicans filibustered three of Mr. Obama’s nominees to serve on the federal appeals court in Washington, which is considered the second most important court in the country because it hears cases involving key federal agencies.

“It’s time to change. It’s time to change the Senate before this institution becomes obsolete,” Mr. Reid said as he pushed his colleagues to coalesce on the critical vote.