"I think we all know from experience you can't make decisions about war and peace based on public opinion," said Sen. Joseph Lieberman, the independent from Connecticut. "Once you commit to a cause, as we did after 9/11, to the cause of a different new Afghanistan and you commit troops to it, you can't be affected by waves of public opinion."
"We are succeeding in Afghanistan today, so I think the downward turn in the public opinion here in the United States has more to do with the understandable preoccupation of the American people with the economy, with jobs, with the deficit," he added.
"In that sense, I think we have to come back and remind the American people of why we are in Afghanistan. Why it is worth it and that we are now succeeding."
President Obama has committed to a draw-down of U.S. troops in Afghanistan, starting July, and transitioning security responsibilities to Afghan forces. Petraeus today said he supports that plan and will present his options and recommendations to the president on how to go about reducing the number of troops.
But that could be a significant challenge in itself. As ABC News reported Monday, field commanders in Afghanistan are asking for more troops and are openly challenging the wisdom of withdrawing any U.S. forces by the July 11 date set by the administration.
There is also concern among Afghans about joining the police and army because of security reasons, despite a hefty salary. On Monday, a suicide bomber posing as an army volunteer blew himself up at an army recruiting center in northern Afghanistan, killing at least 35 people and marking the second such attack on the center.
A broad and bipartisan 73 percent of Americans say the United States should withdraw a substantial number of its combat forces from Afghanistan this summer, but 39 percent think it will, according to ABC News-Washington Post poll.
Some lawmakers plan to draft a resolution calling on the president to withdraw all U.S. forces from Afghanistan no later than Dec. 31, 2011, but that's likely to fail, as it has in the past.
ABC News' Mike Gudgell, Nick Schifrin and Gary Langer contributed to this report.