"Why shouldn't Congress share in the responsibility? If you believe in the War Powers Act, which I do, if you believe in the constitution of the United States that firmly puts in the first article the responsibility for Congress to provide for the general defense, that means we're involved in this discussion--and we should be," he said.
Rogers said the U.S. needs to make it clear to North Korea and Iran that it won't accept the use or proliferation of weapons of mass destruction.
"If you don't send that message, that has real world consequences. This isn't a reality TV show.
At the end of the day, something will actually happen. People will lose their lives. Nations will make a decision moving forward on chemical and biological weapons based on what we do here," he said.
Democratic Sen. Jack Reed of Rhode Island agreed the president "made the right decision" to consult Congress.
"He was very clear that he had not decided on final military action, and then I think he rightfully recognized that in the long run he, the country and the world would be stronger if Congress was supportive of his activities, because this is not just a short term effort, this is a longer term effort," Reed said on "Fox News Sunday."
But fellow Republican Rep. Peter King of New York said the president has been sending "mixed signals" over last 10 days, and his decision to seek input from Congress is a "clear failure of leadership."
"If you feel so strongly about it and if he doesn't want to take the action himself then he should call us back into session tomorrow," King said on "Fox News Sunday." If the vote were held today, King predicted House Republicans would vote "no" over taking military action, though he said he personally would vote "yes."
Congress returns from recess on September 9, but some are calling for lawmakers to come back earlier for a special session so a decision can be made sooner. Rep. Adam Schiff, a senior Democrat on the House Intelligence Committee, urged House Speaker John Boehner to reconvene the House given "the gravity of the situation in Syria."
"Now that the President has called for a vote on a new authorization to use force, it is all the more essential that we be called back into session immediately," he said Saturday in a statement.
Some lawmakers have cited President Ronald Reagan and President Clinton as former commanders-in-chief who acted without asking for congressional approval, saying Obama certainly has the right to do so.
As a former senator, however, Obama was clear on how he felt about the 1973 War Powers Resolution, a law requires the president to seek consent from Congress before force is used or within 60 days of the start of hostilities.
Obama criticized President George W. Bush for not obtaining renewed authorization for the war in Iraq. And as a candidate for president, Obama reaffirmed his stance, telling the Boston Globe in a questionnaire that "it is always preferable to have the informed consent of Congress prior to any military action."
But the president did not seek consent from lawmakers when the U.S. engaged militarily in Libya, nor when Obama expanded the war in Afghanistan. In both instances, members of Congress complained loudly, but the president defended his decision.
While Republican Sen. Rand Paul of Kentucky applauded the president's decision to have Congress weigh in on the Syria issue, he strongly disagreed with the idea of taking military action in the country, saying the situation is too complicated.
"I think the war may escalate out of control and then we have to ask ourselves, who is on America's side over there," Paul said. "If the rebels win will they be America's ally?"
Paul said the Obama administration should engage more effectively with China and Russia, two of Syria's closest allies.
"I think the best outcome for all the major powers would be a peaceful transition in government and Russia could influence that if they told Assad, 'No more weapons," Paul said.
Republican Sen. Jerry Moran of Kansas announced Saturday he also will not support military action.
"America cannot afford another conflict that taxes our resources without achieving goals that advance American interests," he said in a statement.
Republican Sen. Jim Inhofe of Oklahoma, meanwhile, said he doesn't think Congress will approve the president's request and pointed to a weakened U.S. military and potential escalation of violence as major reasons not to intervene in Syria.
"This could be a war in the Middle East," he said Sunday on Fox.
CNN's Tom Cohen, Josh Levs, Greg Clary, Leigh Ann Caldwell, and Dana Bash contributed to this report.