Right wing Christians on the Republican side support a strong Israel. On the other side, most American Jews vote Democratic and support a strong, yet slightly more pragmatic Israel. Collectively, both sides generally agree on varying levels of steadfast support.
The only parts of US politics that diverge from this are extreme right wingers who dabble in anti-semitism and left wing progressives - neither of which have the power or cachet to make any meaningful change in American policy on Israel. As long as this construct remains, there will be no movement on Israeli policy, which is enabled by American moral, materiel, and financial support.
How the Israelis choose to deal with Hamas and vice versa is merely a subset of the broader geopolitical dynamic involving the US supporting Israel because of its own domestic substate politics.