The material was delivered by "rockets which we know the Assad regime has and we have no indication that the opposition has."
Congress resumes work Monday after its summer break, but a heated debate about Syria is already underway.
Vice President Joe Biden planned to host a dinner Sunday night for a group of Senate Republicans.
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.
McDonough plans to meet Tuesday with the House Democratic Caucus.
Obama planned to address the nation on Tuesday ahead of Wednesday's first showdown vote in the Senate over a resolution that would authorize the "limited and specified use" of U.S. armed forces against Syria for no more than 90 days and barring American ground troops from combat. A final vote is expected at week's end.
A House vote appears likely during the week of Sept. 16.
McDonough spoke with ABC's "This Week," CBS' "Face the Nation," NBC's "Meet the Press," CNN's "State of the Union" and "Fox News Sunday." McCaul and Sanchez were on NBC. Cruz appeared on ABC. Rogers and Amash spoke to CBS. Paul was interviewed on Fox. McKeon was on CNN.