Jatropha integerrima

Jatropha integerrima (jat-ROE-fuh  in-teh-GAIR-rih-muh) is a nearly ever-blooming shrub for tropical and subtropical landscapes. The bright red flowers appear in clusters on the ends of the branches anytime new growth is taking place. Individual flowers are about one inch across. Butterflies and hummingbirds find the blooms attractive.
The growth habit is strongly upright, and the tips of the stems may need to be cut back if you want to force side branches. In gardens that experience brief periods of freezing weather, the cold will do the pruning for you. Even if frozen to the ground, plants quickly recover and will be blooming again by late spring. They'll reach 4-5 feet by the end of the growing season.
In frost-free areas, the plant can reach heights of 10 feet or more. Container-grown plants can easily be trained as single-trunk standards.
The leaves can vary from elliptic to deeply lobed. Leaves and stems contain a milky sap that can irritate sensitive skin. All parts of the plant are considered poisonous if ingested, and that may be why it is reported to be deer-resistant.

Jatropha integerrima is native to the West Indies. It is recommended for USDA Zones 10-11, but is freqently seen in warmer parts of  Zone 9b.
This species is drought-tolerant, and does best in full sun to part shade locations. It is supposedly also known as Peregrina or Spicy Jatropha, but I've never heard anyone use those names.