Speaker John Boehner said President Obama has ignored the people and the Constitution.
Twenty-six House Republicans voted to keep the Deferred Action program.
The program provides work permits to people who came to the U.S. illegally as children.
The House will consider funding for the Department of Homeland Security and a bill making changes to the Dodd-Frank law.
Votes on amendments to the DHS spending bill and final passage are expected Wednesday.
The bill would require federal agencies to estimate economic costs of regulations.
Scalise is facing controversy for speaking to a white supremacist group in 2002.
Rep. Marc Veasey (D-Texas) called for a "clean" Homeland Security funding bill without immigration-related riders.
Rebecca Shabad 01/13/15 12:39 PM EST
Lawmakers from both sides of the aisle say it's time to move away from a one-year process.
Rep. Jim McDermott (D-Wash.) noted House members read the Constitution aloud on the floor last week.