In an interview on CNN, Rhodes downplayed polls showing a majority of Americans oppose a military attack and weak support in Congress.
"We think at the end of the day the votes will be there in the Senate and the House," said Rhodes told "New Day" host Chris Cuomo.
Rhodes conceded that it would be a difficult vote for many members of Congress.
"We understand it’s a tough vote for members of Congress but we frankly think it’s important for everybody to come forward and to be counted through that vote because these are tough decisions that we have to make as a country," he said. "We’re not going to win every vote but we believe that at the end of the day we have the strongest case to make that frankly inaction sends a message."
President Obama is asking Congress to back strikes on Syria after that country's regime used chemical weapons on civilians in its civil war. But many lawmakers fear that any attack could lead to a prolonged U.S. intervention or aid Islamist and anti-Western elements in Syria's opposition.
Obama will address the nation Tuesday night to make his case, as the administration makes a full court press to sway lawmakers and the public.
Syrian strongman Bashar Assad in an interview on Sunday denied using chemical weapons, but Rhodes said the leader had "no credibility."
"Assad is the one accountable for the use of chemical weapons by his regime," said Rhodes.