The Obama administration is saturating Congress with classified briefings, meetings and hearings about Syria and its use of chemical weapons, all aimed at winning approval for the measure, but they are far from gathering enough support as public opinion has tipped strongly against intervention.
Obama will speak privately with Senators in his party during the weekly lunch meeting that takes place just outside the Senate chamber.
Obama may also visit House Democrats after the Senate considers the resolution but a leadership aide said "nothing is confirmed at this time."
The Senate could vote as early as Wednesday on a measure that would grant Obama 60 days to utilize limited military force against the Syrian regime of Bashar Assad in retaliation for a chemical weapons attack the administration said killed more than 1,400 people, including 400 children.
While passage of the resolution is in serious doubt in both the House and Senate, a failure in the Senate could doom the measure because the House may become less inclined to bring it to the floor.
As it stands on Monday, fewer than two dozen Senators have come out in favor of authorizing a military strike and 60 will be needed to pass the resolution.
Obama made an impromptu visit Sunday night at the Naval Observatory, where he met for nearly 90 minutes with a half-dozen GOP senators who were dining with Vice President Joe Biden.
Tonight, Obama will make the case for a military strike in a round of interviews on many of the television and cable networks, and on Tuesday he will address the nation.
The push comes in the wake of new polling that shows an increasingly skeptical public.
A CNN/ORC International poll released Monday morning found that seven in 10 Americans believe "a strike would not achieve significant goals for the U.S.," and that it is not in the national interest to get involved.
Obama's visits to the Capitol have been generally infrequent, though he made an appearance on July 31, where he met privately with Democrats in the House and Senate.