Biden and his wife, Dr. Jill Biden, were scheduled to host the senators for dinner as part of the White House's effort to win support for military action in Syria.
The president spent approximately an hour and 20 minutes with Biden and the senators.
The White House said Sens. Lindsey Graham (R-S.C.), Susan Collins (R-Maine), Saxby Chambliss (R-Ga.), Bob Corker (R-Tenn.), Kelly Ayotte (R-N.H.) and Deb Fischer (R-Neb.) attended the dinner.
The Hill's latest whip list counts nine Senate Republicans as "yes/leaning yes" while 14 GOP senators are listed as "no/leaning no."
Ayotte, Chambliss, Corker and Graham are listed as "yes/leaning yes." Collins and Fischer are among 23 Senate Republicans listed as "undecided."
Earlier Sunday, White House Chief of Staff Denis McDonough said lawmakers would vote to authorize military strikes, despite mounting congressional opposition.
McDonough brushed aside the rising number of voices in Congress against military action, saying it was still “too early” to reach conclusions.
“This resolution is going to pass after we work this,” McDonough said on ABC’s “This Week.”
Obama will also conduct interviews with six television networks ahead of a primetime speech on Syria Tuesday night in an effort to win over lawmakers and the public.
Senate Majority Leader Harry Reid (D-Nev.) filed the use-of-force resolution on the Senate floor Friday, setting up a Wednesday vote to end debate and move to final passage. The critical cloture vote will happen on the 12-year anniversary of the 9/11 attacks on New York and the Pentagon and the one-year anniversary of the Benghazi attack.
Another Democratic aide said the vote could happen sooner if Republicans waive certain procedural requirements.
--This report was updated at 9:45 p.m.