President Obama said he wants Congress to hold a “prompt vote” when lawmakers return from recess next week. Politico explains the process behind a vote for military authorization, which can be filibustered in the Senate:

Since Obama is going to Congress with a resolution authorizing the use of military force in Syria rather than ordering military strikes first and then informing Congress, as required under the War Powers Act, the use-of-force proposal will be fully debatable and amendable. Under the War Powers Act, a use-of-force resolution would face only limited debate and require a simple majority vote.
The revised proposal can be filibustered by those opposed to any U.S. involvement in Syria’s two-year-old civil war, meaning Reid will need 60 votes to overcome opposition to the measure. Some Senate Democrats, such as West Virginia Sen. Joe Manchin, have publicly stated that they do not support Obama’s position on Syria. With only 54 Senate Democratic votes to play with, Reid and the White House cannot afford many Democratic defections.
Top Senate Republicans, including Minority Leader Mitch McConnell and Minority Whip John Cornyn , have yet to say how they will vote. How many of the 46 Senate Republicans will vote for the Syria AUMF is difficult to estimate at this point. A Democratic aide suggested Reid and Obama “would be lucky” to get 10 to 15 Republican votes for the measure.