Sen. Ted Cruz tried to get the Senate to consider a measure Thursday providing that any American who joins the fight with terrorist groups such as the Islamic State would immediately renounce their U.S. citizenship, but a Democratic senator objected, saying more time is necessary to weigh the significant constitutional issues it raises.

Ahead of the Senate’s scheduled consideration Thursday afternoon of a proposal to arm and train Syrian rebels, part of President Obama’s strategy to combat the terrorist group, the Texas Republican asked for unanimous consent to pass the Expatriate Terrorist Act he introduced earlier this month.

The measure makes providing support to or fighting for a terrorist group targeting the U.S. “an affirmative renunciation of American citizenship,” Mr. Cruz said on the Senate floor Thursday. He pointed out that former Sens. Joe Lieberman, Connecticut independent, and Scott Brown, Massachusetts Republican, introduced a similar measure several years ago related to al Qaeda.

“If we do not pass this legislation, the consequence will be that Americans fighting alongside ISIS today may come home tomorrow with a U.S. passport, may come home to New York or Los Angeles or Houston or Chicago and innocent Americans may be murdered if the Senate does not act today,” Mr. Cruz said.

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