It would have to be 5 doors as the only 3 doors on the US market are the Mini, Honda CR-Z, Hyundai Accent and the Toyota Yaris.

A 5 door hatch series would be as follows with a 1.6L engine size cap:

Chevrolet Aveo, 1.6L Ecotec
Toyota Yaris, 1.6L 4ZR-FE
Honda Fit, 1.6L R16A (sourced from overseas model Honda Civic)
Suzuki SX4 Sportback, 1.6L J16
Ford Fiesta, 1.6L Duratec Ti-VCT (Sigma engine family)
Dodge Caliber, 1.6L Tritec engine (sourced from Euro-spec Chrysler PT Cruiser. It's a engine used in the Mini Cooper from 2001-2006)
Nissan Versa, 1.6L HR16DE (sourced from the Nissan Versa base model sedan)
Mini Countryman, 1.6L Prince turbo
Kia Rio5, 1.6L Hyundai Alpha 2
or
Kia Soul, 1.6L Gamma