The White House has tied any new deal on young undocumented immigrants to a clampdown on illegal immigration, including a border wall with Mexico.
US President Donald Trump is asking for funding for the wall, speedier deportations and the hiring of thousands of new immigration officials.
Last month he ended the Obama-era “Dreamer” programme which had protected some 690,000 immigrants.
Leading Democrats in Congress have rejected the latest proposals.
They accused Mr Trump of backtracking on a commitment not to include the border wall in negotiations over the status of young immigrants, who are mostly from Mexico and other Latin American countries.
The Deferred Action for Childhood Arrivals (Daca) programme, set up in 2012 under President Barack Obama, is due to expire in March, casting doubt on the future of those protected.