For his part, Obama sought to persuade Americans of the opposite -- that the diplomatic stirrings by Russia and Syria occurred because of the credible threat of a military attack intended to deter Syria from using its chemical weapons again.
The president has not said whether he would launch strikes without the support of Congress.
Meanwhile, a bipartisan group of eight senators is working on an alternative resolution to the one authorizing military action already passed by the Senate Foreign Relations Committee. It would include "guidelines, reporting process and benchmarks that have to be met," McCain told CNN.
On the House side, Democratic Rep. Chris Van Hollen of Maryland said he was working on a version of a resolution that would authorize a military response if the diplomatic process failed to yield an acceptable result in 30 days.
The Obama administration has launched a sweeping lobbying effort, with the president meeting on Capitol Hill on Tuesday with senators from both parties as part of a series of classified briefings, hearings and other consultations on the Syria issue.
Since Friday, the administration has spoken with at least 93 senators and more than 350 members of the House, a White House official said Tuesday.
Despite such outreach, indications were that the congressional push wasn't working.
Sen. Mitch McConnell, the top-ranking Republican in the Senate, announced Tuesday he will vote against authorizing military action on Syria.
So did Democratic Sen. Ed Markey of Massachusetts, who won the seat vacated by Kerry when he became secretary of state.
A running CNN vote count showed most members of Congress remained undecided, with significant opposition in both chambers among the much smaller numbers who have announced their decision leaving the outcome in doubt.