Chances for a broad immigration deal emerging from Congress this year are all but dead after the Senate within a span of a few hours on Feb. 15 rejected both a White House-backed proposal and a bipartisan compromise to address the fate of 1.8 million young immigrants.

The stalled debate left lawmakers in both parties looking for a way out and the immigrants known as dreamers still facing a deportation threat unless a court intervenes. President Donald Trump showed no sign he would bend on his demands for cuts to legal immigration as his administration made all-out effort to kill...