Manchin asked West Virginia residents to send advice either by email, Twitter or via Facebook.
Several Syria hearings are scheduled this week with top administration officials who are hoping to convince members to support a war authorization resolution. The vote on the resolution will likely take place next week.
Earlier in the day, House Speaker John Boehner (R-Ohio) said he would vote in favor of military intervention but also said it would be up to President Obama to win the votes in Congress.
Sen. John Cornyn (R-Texas) went further on Tuesday by calling on President Obama to address the American people directly on why he wants to attack Syria.
"I appreciate President Obama holding a meeting today at the White House," Cornyn said. "Unfortunately, many questions are still left unanswered. I would urge the president to make the case not only to Congress, but to the American people, in a national address.
"The president needs to explain in detail what vital national interests are at stake, his plan for securing these interests and a clear definition of what success looks like in Syria."