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With a bad cam phaser, which advances and retards camshaft timing for engine performance and emissions, I would not go too long. It will eventually cause engine performance issues, and especially catalytic converter damage if it is ignored too long. And if it eventually breaks, it can cause severe internal engine damage,
The 5.4L engine is highly dependent on oil pressure. We have seen the cam phasers break and send the trigger wheel which is attached to the phaser break off and fall into the engine where the timing chain is and cause the timing chain to jump time which will cause the valves to hit the pistons and cause extensive engine damage. The trigger wheel is what the cam sensor read off of on the front of the engine on the timing cover/front engine cover. If it sounds like a diesel engine, oil pressure is a problem and I would recommend inspecting the engine valve train by removing the valve cover and looking at the rocker arms, camshaft and the camshaft cam caps that hold the cams to the cylinder heads for scoring. There are no bearings on the camshaft. Only a machined surface with oil galleys that allow the camshaft to get oil.