OHV or L-head motor? What make? Air or liquid cooled?
On older OHV engines the valve guides can let a bit of oil into the cylinder and it will blow white smoke for a few minutes. Also, if the machine was tipped or overfilled with oil, the crankcase breather can spit oil into the air cleaner housing, getting it into the carburetor and soaking the air filter, choking it off. The crank breathers usually have a reed valve in them to keep a slight vacuum in the crankcase (to keep the oil from blowing past the seals) and it has a hose routed to the air cleaner housing. Confirm your oil level is correct, and check the air filter and look for oil in the air filter housing.
If you have a liquid-cooled machine (some Hondas), you could have a coolant leak.