"What is the best way to get the president to act? Well, my friends, you know. That's you. When Republican senators protest what the president has done, he sometimes acts," Schumer said of the Senate floor.
Paul, a libertarian-leaning GOP senator, argued that if Congress will pass a resolution opposing Trump's Syria decision, it must have a major war debate.
"If the Democrats want to send our young men and women to fight in the Syrian civil war, let's have that debate. Let's have the constitutional debate today on the Senate floor right now," Paul said.
It also urges Turkey to end its military operation, calls on the United States to protect the Kurds and urges the White House "to present a clear and specific plan for ISIS's permanent defeat."
It is the second time Paul is blocking the resolution from getting a vote. Schumer made the same request last week before the Kentucky Republican held it.
Schumer argued on Tuesday that Paul's understanding of what a declaration of war requires is "different from 99.9 percent of America and of every other person in the House."
Paul shot back that if the United States tried to "create a Kurdish homeland … hell, well, we need a debate and a vote and approval of power."
"It's a complete mess," he added. "It's time we get the hell out."
But the GOP leader has panicked the elected parliament and introduced his own competing measure on Tuesday.
McConnell said the house measure was "badly inadequate." He added that it was "silent" about the US military presence in Syria and that "perhaps the goal was to print disagreements within the Democratic Party."