"The mission should be defeating ISIS before they succeed in carrying out more horrific acts of terror, before they succeed in murdering Americans. If need be, we should go that step," Cruz told "This Week" anchor George Stephanopoulos when asked whether U.S. troops on the ground should be considered.
Cruz, however, emphasized that the first steps in combating the terror group should be arming the forces already battling ISIS on the ground, and stepping up the severity of air strikes.
"We need to arm the Kurds and we need to use the Peshmerga as boots on the ground. They're effective. They're ready. They're our close allies and we need to use that in close coordination with overwhelming air power to take out ISIS," Cruz said. "We've seen essentially photo-op foreign policy, where we drop a bomb here or a missile there."
"It's time for Senator Cruz and Senator [Jeff] Sessions and Senate Republicans and Senate Democrats to stand with the American people and to block the president's actions," Boehner said Tuesday.
But on Sunday, Cruz denied responsibility for the plan to block DHS funding, saying it was the strategy of House leaders.
"This was not my plan. This was leadership's plan. This was the Cromnibus, which you'll recall in December, I fought vigorously against it. I said, this plan doesn't make sense. It gives away all our leverage, and it's a plan that is designed to fail. So, I would ask leadership, this is their plan they designed. Let's see what their next step is," Cruz said.
"And Republicans, what we need to do is we need to honor the commitment we made to the voters, and that means we need to fund DHS and we also need to act effectively to stop President Obama's illegal and unconstitutional executive amnesty," Cruz added.
"Look, Jeb Bush is a good man. He's a good governor. I respect him," Cruz said. "If he chooses to run, it certainly looks like he's going to, he's going to have to make the case to Republican primary voters, concerning his record, concerning certainly his support for Common Core, concerning his policies on immigration, and I think we'll have a debate on that."
"If Hillary Clinton wants to run by telling Americans that the economy is doing great and you can credit President Obama and Hillary Clinton for that, I would encourage her to follow that strategy," Cruz said. "I'm glad President Obama and Hillary Clinton have discovered income inequality because it's increased dramatically under their failed policies."