House Homeland Security Committee Chairman Mike McCaul (R-Tex.) on Sunday cautioned the Obama administration against taking a "victory lap" over the deal last week to rid Syria of its chemical weapons.

The congressman gave credit to Russia and expressed skepticism that the threat of an "unbelievably small" military action against Syrian government forces, as Secretary of State John Kerry put it, prompted the Assad regime to buy into the agreement.

"I don't think this is a time for the White House to be boastful," McCaul said. "I quite frankly think what won the day here is that [Russian President Vladimir Putin] looked in his own backyard and realized that these policies that he saw in Egypt and Libya were going to happen in Syria, which could potentially fall to the Muslim Brotherhood and the extremists. He decided it was time to step in and try to fix the problem."

McCaul also said Russian troops should lead the effort to secure Syria's chemical weapons and protect U.N. inspectors in that country. "From a security standpoint, it's going to be a huge concern," he said, noting that rebel extremist elements may try to take over some of the chemical arms as the process moves forward.