Nah, you could definitely do that with an electric motor and propeller, but the power requirements will be very high. Ballparking the math here...
Mass flow rate will be the product of air density, area, and velocity through the prop. Thrust force is the product of mass flow and velocity. Therefore, F = ρav2. Rearranging this and solving for the discharge velocity to achieve 35lbf through 1 square foot, you get 37 m/s (or about 83 mph). This is high, but definitely doable with a propeller. The power in this jet will be one half the product of the mass flow rate and the exhaust velocity (this is just the rate of kinetic energy addition to the jet), which for this example gives 2.88 kW. Propellers are not perfectly efficient though (80% or so is probably achievable with one optimized for this case), so you'd actually need about 3.5-4kW of shaft power to achieve this level of thrust. It's not impossible, but it will be loud, and it will have an 83mph jet of air coming out the bottom at all times (which may or may not be a problem, depending on the intended application).
To show how much this is impacted by the disc area, a 1 square meter rotor area gives 11.3m/s (25mph) discharge, with a jet power of 878 watts and a required motor power of a bit over a kilowatt.