There are a lot of potential variables to consider in developing a casualty estimate for a potential large-scale intervention. Senators John McCain and Lindsey Graham have floated various proposals to deploy 10,000 U.S. ground combat troops to both Iraq and Syria, with the most recent calling for 10,000 in Syria along with 10,000 Arab allies.
It is not clear if McCain, Graham, or Obama are assuming a U.S.-led ground offensive to be followed by the withdrawal of U.S. troops, or a ground offensive and an open-ended stability/peacekeeping mission. Nor is it clear if they assume an offensive against Daesh only or an attack on the Assad regime as well.
Potential ground offensive scenarios:
1. 10-20,000 U.S. advisors only in Iraq and Syria
2. 10,000 U.S. troops leading a ground offensive against Daesh in Iraq
3. 10,000 U.S. troops in Iraq and 10,000 U.S. troops in Syria leading a ground offensive against Daesh only
4. 10,000 U.S. troops in Syria and 10,000 Arab coalition troops leading a ground offensive against Daesh only
5. 10,000 U.S. troops in Syria and 10,000 Arab coalition troops leading a ground offensive against Daesh and the Assad regime
A long-term stability and support operation in Syria would almost certainly require more than 10,000 U.S. and 10,000 Arab coalition troops, even if it were confined to areas currently held by Daesh, and even more if extended into former Assad regime areas.