The Marvel-Schebler TSX458 won't need to be replaced. They are a simple updraft, pressure balanced design that is rebuildable and parts are readily available.
Before you do anything, make sure you have adequate fuel flow to the carb.
Pull the plug on the fuel bowl and hold a container under it to catch the gas. It should gush out like a cow peein' on a flat rock. If it doesn't then you''l have to find out why. There's a filter in the fuel inlet elbow( screen) so start there.
If you have adequate fuel flow, I'd try to set the idle speed with the throttle lever adjustment screw first. it should idle at 400-450 rpm(spec is 400 rpm). It's cunningly designed so that when the engine is hot put you can burn yourself on the exhaust manifold as you try to adjust the idle speed. So hook up a dwell tach to read rpm, start the engine and let it warm up. Since your engine dies when you move the thottle in the idle position, do that and then reach around the backside of the carb with a screw driver and turn the screw CW one full turn. Start up and see if you can now hold idle with the throttle at idle. Repeat til you have the required idle speed.
If that doesn't work, you may have to set the idle mixture first. You do that by getting the lowest speed you can run at with a warmed up engine leaning or enriching the idle mixture screw on the neck of the carb to get the highest rpm and then set the lowest rm with the throttle adjustment screw. The idle mixture scre actually controls idle air so screwing it in enriches and screwing it out leans. If it has no effect, you have a clogged passage and the carb needs to come off for a thorough cleaning.
If you problem is at high rpms then the power jet may need adjustment. Screw the power jet knob( big screw on top of fuel bowl) down all the way but don't reef it down or you'll damage the needle.Open it to 1-1/4 turns. Start the tractor and let it warm up.Move the throttle quickly to accel from idle to max rpm. the engine should accellerate smoothly to high speed. if it stumbles open the main jet 1/8 turn and see if that helps. If you see carbon come out of the exhaust then the mixture is too rich and lean it some. accel again ad see if that helps. It's a trial and error process.
DO NOT ADJUST THE NEEDLE BELOW ONE FULL TURN OUT. The engine needs a slighly enriched mixture for charge cooling and running too lean can burn the exhaust valves. if that doesn't work, again pull the carb for a thorough cleaning.
