The discovery of large superconducting transition temperature of T_c=190 K in metallic H₂S under high pressures of 200 GPa, has renewed the interest in the superconducting properties of metal-hydrogen systems. These materials are expected to be electron-phonon superconductors and hydrogen with its low mass can contribute new optic phonons that may couple with the conduction electrons. Often, though not always, a large electron-phonon coupling parameter λ (and consequently high T_c) can result from a high electronic density of states at the Fermi level (N(E_F)) and the presence of soft phonons. Our first-principles calculations of cubic TiH₂ which has a large 3d N(E_F)=2.8 states/eV/f.u. Our calculated phonon dispersions show that Ti modes active below frequencies of 10 THz whereas much lighter H modes are active between 32 and 40~THz. Electron-phonon coupling calculations reveal a λ=0.98 which corresponds to a T_c=6.1 K. However, the large N(E_F) also leads to a tetragonal instability at low temperatures in TiH₂, which may be overcome by a uniaxial strain, potentially making it a candidate for electron-phonon superconductor.