WASHINGTON — It was perhaps the one topic that received bipartisan attention Tuesday night — from President Obama during his State of the Union address, in the official Republican response delivered by Senator Marco Rubio of Florida, and in the Tea Party’s response to the response: the need to overhaul the nation’s immigration laws.

But despite the bipartisan call for broad action, partisan divides on how the topic should be tackled were on display Wednesday as the Senate held its first substantive hearing on the path forward.