The issue described occurs when the vehicle is idling, characterized by shaking and a sensation that the engine might shut down. This problem does not persist while driving, indicating it's likely related to engine performance at low RPMs. The additional symptom of burning oil suggests that the engine is consuming more oil than normal, which can be identified by a low oil level, the smell of burnt oil, or smoke from the exhaust. These symptoms can affect the vehicle's performance by reducing engine efficiency, potentially leading to increased fuel consumption and decreased acceleration. The shaking at idle can also cause discomfort and raise concerns about reliability and engine health.

The likely root cause of these symptoms could be worn engine components, such as piston rings, valve seals, or a malfunctioning PCV (Positive Crankcase Ventilation) system. Worn piston rings or valve seals can allow oil to seep into the combustion chamber, burning oil during operation. This would not be as noticeable when driving at higher speeds due to increased engine efficiency and combustion. A faulty PCV valve can cause excessive crankcase pressure, leading to oil leaks or oil being pushed into the intake manifold. If not addressed, this issue can lead to significant engine damage, including but not limited to, overheating, reduced engine life, and in severe cases, engine failure.