The source said Miller has injected himself into talks between lawmakers and is making the issue more difficult by coming to the table with unreasonable demands on behalf of the White House.
Miller is adding "a bunch of stuff that will be non-starters with Dems and divide GOP," the source said.
President Donald Trump announced the end of the Deferred Action for Childhood Arrivals program, known as DACA, last month. But he delayed termination of the program by six months to allow Congress time to come up with legislation to determine what to do with the nearly 800,000 young undocumented immigrants who were brought to the US as children.
But the White House proposal pushed by Miller comes nowhere near a clean DACA fix as it adds other controversial immigration proposals, the source said.
Among the White House "principles" in exchange for a DACA fix that Miller and the White House are asking for include making it more difficult for legal residents of the US to bring in family members from their counties of origin. This measure is opposed by Democrats and divide even Republicans.
There are also principles outlined in a rebranded version of the proposed SAFE Act, a highly controversial bill from 2013-2014. These measures would give state and local law enforcement boards authority to enforce immigration laws, allowing states to craft their own immigration rules and potentially criminalizing anyone who is here without legal status.
"Think Sheriff Arpaio," the source said, referencing the controversial former Arizona sheriff who became known for his treatment of those he held in an outdoor jail known as "Tent City," where he made people wear pink underwear and work in chain gangs.
The White House has also discussed requiring Congress, not the Department of Homeland Security, to handle designating Temporary Protected Status for immigrants. TPS is a a provision of immigration law that allows the government to grant temporary work authorizations and protection from deportation to immigrants, including otherwise undocumented ones, from certain countries where life remains dangerous. Conditions that could merit the status include armed conflict and civil war, natural disasters, epidemics and "other extraordinary and temporary conditions."
This measure alone, the source warned, would kill any DACA fix if it's included.
The White House is also calling for billions of dollars in border security, the source added.
"This stuff will piss off Dems and divide Republicans," the source told CNN.
A message left with Miller seeking comment was not returned. White House spokesperson Raj Shah told CNN that priorities "will reflect the needs that professionals in the agencies and departments have expressed to us are the tools, resources and authorities needed to secure our border and keep the American people safe."
Democrats support the Dream Act
, which would protect eligible young immigrants who arrived as children and put them on a path to citizenship. They say they could accept border security as a compromise with it, but insist they will not vote for anything that could put the families and friends of those protected at greater risk of deportation.
But Republicans are also insistent that any DACA deal must include border security and likely immigration enforcement measures, and the more conservative members of the party are suggesting certain policies -- including mandatory worker verification, cuts to the legal immigration system and expanded deportation authority -- that would be almost impossible to get Democrats to agree to.
Miller has worked as a key voice in Trump's ear on immigration
, along with Steve Bannon, the former White House chief strategist who now runs Breitbart News. He was a key architect of Trump's travel ban, which has been criticized for targeting Muslim-majority countries.