Updated

As Congress returns to Washington from its August recess, the White House is putting a sharp edge on its pitch for support for a possible military strike on Syria -- challenging members to act on indisputable evidence of a recent chemical attack on Syrian residents and suggesting Iran and Hezbollah are watching.

Members of Congress “do not dispute the intelligence when we speak with them,” White House Chief of Staff Denis McDonough told “Fox News Sunday.” “The question then becomes should there be consequence for this? The Iranians are going to watch that answer. The Syrians are going to watch that answer. Hezbollah is going to watch that answer.”

McDonough appeared on all five Sunday talk shows, with President Obama ready to make a prime-time appeal Tuesday for public support and the Senate set for a significant vote on the issue as early as Wednesday.

A House vote appears likely during the week of Sept. 16.

The administration has essentially been on an all-out campaign to win support after Obama told the nation Aug. 31 that the United States should punish Syrian President Bashar al-Assad, whom he thinks ordered a chemical attack earlier in the month that killed nearly 1,500 of his own people, and that he wants congressional support for a limited military strike.

Still, McDonough allows the administration lacks "irrefutable, beyond-a-reasonable-doubt evidence" that skeptical Americans are seeking.

"The common-sense test says [Assad] is responsible for this,” McDonough said. “He should be held to account.”

The tally of those killed by chemical weapons is scant compared to the sum of all killed in Syria’s roughly 2-year-long civil war: more than 100,000, according to the United Nations.

In an interview Sunday, Assad told CBS reporter Charlie Rose there is not conclusive evidence about who is to blame for the chemical weapons attacks and again suggested the rebels were responsible. The interview is to be released Monday morning.

Asked about Assad's claims there is no evidence he used the weapons, Secretary of State John Kerry told reporters in London: "The evidence speaks for itself." Kerry held a joint press conference with United Kingdom Foreign Secretary William Hague and was due to return to Washington to brief Congress Monday afternoon.

Kerry's predecessor as Secretary of State, Hillary Rodham Clinton, is scheduled to speak Monday at a White House event on wildlife trafficking and plans to reiterate her support of Obama's efforts to pass the Syria resolution, according to a Clinton aide who spoke to the Associated Press on condition of anonymity because the person was not authorized to speak publicly.

Earlier Monday, Russian foreign minister Sergey Lavrov and his Syrian counterpart Walid al-Muallem urged the United States to focus on convening a peace conference as opposed to military action, with the latter diplomat accusing President Obama of backing terrorists, according to Reuters.

Obama has scheduled six network interviews on Monday, including one with Fox News, then a 9 p.m. White House speech Tuesday. Hours before the speech, Obama is due to meet with Senate Democrats to attempt to shore up their support. On Sunday night, Obama dropped in on a dinner held by Vice President Joe Biden at the Naval Observatory in Washington. Six Republican Senators, all thought to be ambivalent about the idea of military action in Syria, were treated to a family-style meal of Italian food.

Obama faces a tough challenge on Capitol Hill, especially in the Republican-led House.

A survey by the Associated Press shows that House members who are staking out positions are either opposed to or leaning against Obama's plan for a military strike by more than a 6-1 margin.

"Lobbing a few Tomahawk missiles will not restore our credibility overseas," Texas Republican Rep. Mike McCaul, chairman of the  House Homeland Security Committee, said on NBC’s “Meet the Press.”

He was joined by Rep. Loretta Sanchez, D-Calif., who said, "For the president to say that this is just a very quick thing and we're out of there, that's how long wars start."

Almost half of the 433-member House and a third of the 100-member Senate remain undecided, the AP survey found.

"Just because Assad is a murderous tyrant doesn't mean his opponents are any better," Texas Republican Sen. Ted Cruz said on ABC’s “This Week.”

In addition of Obama and McDonough’s efforts, a U.S. official on Saturday released a DVD compilation of videos showing attack victims that the official said were shown to senators during Thursday's classified briefing. The graphic images have become a rallying point for the administration.

Vice President Joe Biden planned to host a dinner Sunday night for a group of Senate Republicans. And Obama's national security adviser, Susan Rice, plans to discuss Syria in a speech Monday at the New America Foundation and later meet with members of the Congressional Black Caucus.

Bipartisan, classified briefings for Congress are set for Monday and Wednesday. And McDonough plans to meet Tuesday with the House Democratic Caucus.

Republican Sen. Rand Paul, of Kentucky, told Fox that he would consider a filibuster, but noted the delay tactic was unlikely to permanently nix a vote.

Paul would, however, insist his colleagues consider an amendment to the resolution that would bar Obama from launching strikes if Congress votes against the measure.

 The Associated Press contributed to this report.