Undocumented residents could apply legally for jobs and join American society, but not vote.
The US President promised to work constructively with Republicans in Congress for the next two years.
President Barack Obama was dealt a punishing blow that will limit his legislative agenda.
Obama and other officials are travelling around the country to promote the new healthcare plan.
The agreement includes income verification for those seeking subsidies under the 2010 healthcare law.
The Senate is scheduled to meet at noon on Wednesday.