CSA attacks and attempts to conquer portions of Mexico, the US almost guaranteed will intervene as per the Monroe Doctrine, Mexico pushing for territorial concessions from the CSA will bother the US, who feel that they had a lot of hard-earned work going into settling all those Mexican Cession territories and that they aren't just going to give em back.
Okay, I hate to be the bringer ofbad news, but the Monroe Doctrine would have no bearing on this. The Monroe Doctrine specifically stated that no European powers could interfere with the development of North and South America. The CSA does not constitute a European power.
Furthermore, the Monroe Doctrine, until the 20th century was supported heavily by Britain. Without their support, the US doesn't have a proverbial plank to stand on.
Pushing it even furter, the CSA would be fighing, most likely, against Maxamillian; a foreign 'Emperor' imposed by European powers. The CSA would be the nation most likely to claim that the Monroe Doctrine relates to them, as the are fighting to return Mexico to a civil government; if they ask for compensation, that is only fair.
After the Civil war, as much as the US wants revenge, its most likely going to be dominated by the copperhead Democrats who want to see CSA cotton flowing to their mills. Also, they are going to be very unlikely to alienate Britain which will be a supporter of the Confederacy.
Most likely, you end u pwith a straight up war with the CSA 'helping' to topple the Habsburg Emperor and demanding territory as compensation. The Conferdacy gets what it wants, but has to deal with rebel forces which, likely, are being supplied by the USA (although there is no evidence to support this assumption)