WASHINGTON — The Senate Foreign Relations Committee voted Thursday to authorize the military campaign against the Islamic State, a party-line decision that raises difficult questions for Republicans and intensifies a debate over war powers that has split President Obama from many in his own party.

The 10-to-8 vote put on display an unusual alliance between some Democrats and some Republicans as well as contemplations about morality, obligation, constitutional prerogatives and the proper balance of power between branches of government. It was also a foreshadowing of a debate likely to be held on the Senate floor after the Republican-controlled Congress returns in January.

All Democrats voted in favor of the measure that would authorize Mr. Obama’s war against the Islamic State, also known as ISIS or ISIL, but greatly restrict the use of ground forces and limit the operation to three years before Congress has to revisit it. Opposed were all the Republicans, seven of whom warned of binding the hands of the commander in chief. One Republican, Senator Rand Paul of Kentucky, voted against the measure for a different reason, which, he said, is that the restrictions did not go far enough.

Senator Robert Menendez, the New Jersey Democrat who leads the committee, said that Mr. Obama should not have the sole power to send the nation’s young people to dangerous overseas conflicts. He rejected the idea that “Congress should just succumb to what the executive wants.”