Rahall said Jenkins was trying to politicize a serious military issue.
Although other members of the national delegation have said they do not support a missile strike, some have supported actions condemning Syria's possession of chemical weapons in the past.
The Syria Accountability and Lebanese Sovereignty Restoration Act of 2003 passed Congress with nearly unanimous support. Sen. Jay Rockefeller, D-W.Va., and Rep. Shelley Moore Capito, R-W.Va., both voted in support of it.
Then-Sen. Robert Byrd, D-W.Va., was one of the few senators to vote against the bill.
On two other occasions Capito has co-sponsored legislation that called for greater U.S. involvement in Syria.
In 2007 and 2009, she co-sponsored the Syria Accountability and Liberation Act. The two pieces of legislation were similar in their calls for increased economic sanctions against Syria.
Both also pledged U.S. support to independent groups that would dismantle Syria's chemical weapons during a transition to an internationally recognized democratic government.
Neither bill called for U.S. military action, and neither came close to becoming law.
Monday, Capito announced she did not support a missile strike in Syria. Capito spokeswoman Lisa Boothe said the congresswoman has been consistent in her opposition to military action in the country.
Her support of the previous legislation was intended to isolate Syria through economic sanctions and "block the regime's use of chemical weapons," Boothe said in an email.
Fellow Republican Rep. David McKinley was not in Congress at the time the legislation was introduced. In 2011 though, he co-sponsored the Syria Freedom Support Act. The act called for actions very similar to those outlined in the two bills Capito co-sponsored.
McKinley has repeatedly said he doesn't support a strike. A spokesman did not return a request for comment Tuesday as to why he supported the 2011 legislation.
Sen. Joe Manchin, D-W.Va., also opposes a strike. He is pushing a plan, created with Sen. Heidi Heitkamp, D-N.D., that would call on Syria to quickly sign the Chemical Weapons Convention.
During that time, the Obama administration would need to come up with a detailed plan for a course of action if Syria did not sign the convention.
The convention prohibits the production, stockpile, transfer or use of chemical weapons. Close to 200 countries have signed. It closes "loopholes" in the Geneva Convention — which also prohibits the use of chemical weapons and was signed by Syria — Manchin said Tuesday in a Senate floor speech.
Rockefeller, who previously led the Senate Select Committee on Intelligence, hasn't said whether he would support a missile strike in Syria. During a recent event he briefly discussed his decision making process.
"I've been to Syria many times. I've met with Assad a number of times, and I know the intelligence about them very, very well," Rockefeller told the Sunday Gazette-Mail.
"It's a careful decision because of two parts: If we do something, what risk do we run? If we don't do something, what risk do we run?"
Rockefeller said last week he planned to announce his decision on a potential missile strike Monday or Tuesday. A spokesman said Tuesday afternoon the fluid nature of the situation necessitated more time for the senator to decide.
The Associated Press contributed to this report.