For his part, committee chief Rep. Buck McKeon (R-Calif.) said Congress and the White House have more work to do with Moscow, to see if the plan can become reality.
"Its hard to say at this point" whether Washington and Moscow can be confident enough to guarantee the Russian disarmament plan will work, McKeon added.
Their comments came after House defense and intelligence committee members were briefed by White House officials on the administration's case for military action in Syria.
Before Monday's latest round of congressional briefings on Syria, Russian Foreign Minister Sergey Lavrov told reporters Moscow would press Syrian president Bashar Assad to place his chemical weapons arsenal under international control.
Russia is one of Assad's key allies in the international community.
Syria's foreign minister, Walid al-Moallem, welcomed Russia's proposal regarding the country's chemical stockpiles, according to multiple media reports.
Should Assad agree to the plan, the move could be enough to dissuade Washington from carrying out military strikes against the regime's forces.
Secretary of State John Kerry was initially doubtful Assad would comply with the plan.
"Turn it over, all of it, without delay. And allow the full and total accounting for that, but he isn’t about to do it,” Kerry said at a London press conference.
Those administration doubts over the Russia plan were also made clear to defense lawmakers during Monday's briefings.
For his part, Senate Armed Services Committee chief Carl Levin (D-Mich.) said Congress and the White House "shouldn’t get our hopes up too high" that Syria will agree.
"If Russia is serious, and not just helping Syria stall, it could make a difference," Levin said in a statement Monday.
The White House is "rightfully skeptical" of the plan, Smith said, given Moscow's military and political ties to the regime.
That said, Smith noted that administration officials should pursue all diplomatic solutions, including the Russia plan, to end the current stalemate with Syria.
The Russia plan is the first effort by Russia to end the U.S. standoff with Syria.
U.S. forces are poised to launch targeted strikes in the country pending congressional authorization, in response to Assad's reported use of chemical weapons against anti-government forces in the country.
Use of those weapons crossed a so-called "red line" set by President Obama, which he said would trigger an armed response.
Last week's vote by the Senate Foreign Relations Committee to authorize the use of force in Syria was key in prompting the Russia offer, Sen. Bob Corker (R-Tenn.), the panel's ranking member, said Monday.
"Had we not done what we did last week," Moscow would have never made its proposal to Syria, Corker told reporters.
Panel members approved military action by a vote of 10 to 7 last Wednesday.
Seven Democrats and three Republicans backed the measure, while five Republicans and two Democrats on the committee opposed it.
Obama has maintained the White House has the authority to carry out strikes against Syria without the blessing of Congress.
However, the president opted to seek lawmakers' approval, to ensure any action taken has the full support of the American people.
In the U.S., finding support on Capitol Hill has proven difficult, with members in both parties saying they want to avoid getting the U.S. involved in another conflict in the Middle East.