Russia has loaned out a lot of money to Assad and has basing rights through his regime, and needs him as head of government in order to preserve their financial and strategic interests. Our current reading is that they're basically reserving their place at the table if/when Syria is partitioned with 'facts on the ground', with the hopes of having a friendly regime in at least some of the useful parts of Syria.
US wants to preserve some semblance of order and Iraq, at least enough so that the Kurds (who the US support right now) will get on board with federalism instead of succession to form a Kurdistan nation-state. The executive branch was willing to ignore Assad until chemical weapons were used, violating the international norms the US supports, but the legislative branch responding to the will of the people at the time prevented an escalation of military force out of fear of becoming entrapped in another Middle Eastern quagmire. That said both branches want something done about Assad, so we're left with a 'just the tip' policy.
Iran and the Gulf States are at cross purpose as Iran wants to set up a Shia hegemony while the Gulf States want to set up a Sunni hegemony. The US used to be interested in Saudi Arabia for the oil, but now-a-days most US oil comes from North America so it's main interest is to keep Suadi Arabia from feeling threatened enough to start properly militarizing and pursuing a nuclear weapons program.
The Kurds are wanting to do what's best for the Kurds, which means keeping ISIS out of Kurdistan and picking their battles to keep from being overstretched. However, the government of Iraqi Kurdistan and the YPK(?) are at cross purpose in the long term as the Iraqi Kurds want European socialism while the Syrian Kurds want a Marxism that comes uncomfortably close to Leninism.
The US and Turkey are at cross purpose because of the Kurdish issue (the Turkish Kurds are fighting the Turks), but the US can't tell Turkey to shove off due to Turkey being a NATO member and having control of strategically important shipping channels.