It's not clear if the Ryan bill has enough GOP votes to pass, and the conflicting statements from the White House on Friday may put it on even shakier ground.
"I'm looking at both of them", Trump said when asked about the proposals during an impromptu interview on Fox News' "Fox & Friends", adding: "I certainly wouldn't sign the more moderate one".
Mr Shah said that, in the interview, Mr Trump had been voicing opposition not to either of those Bills, but to a "discharge petition", a rarely used procedural manoeuvre House Republicans had threatened to employ that would have forced debate on four immigration Bills, including a popular bipartisan one that is opposed by Mr Trump, Mr Ryan and House conservatives. Trump's comments sent lawmakers into a last-minute tizzy as they prepare for potential votes in the coming week.
Both the Republican Bills under discussion, which have been blasted by Democrats and immigration advocacy groups as being too harsh, would fund the wall that Mr Trump wants to build on the US' south-west border with Mexico.
Two White House officials said Short disclosed his plans Friday.
But White House spokesman Raj Shah clarified Friday evening that the president had been commenting on the separate - and now abandoned - effort by moderate Republicans to push votes on other legislation.
Under the bill, jurisdictions that decline requests from federal immigration authorities to detain undocumented immigrants in their custody could face lawsuits if an immigrant they release commits murder, rape or sexual abuse of a child.
House Minority Leader Nancy Pelosi, D-Calif., called the Trump policy "barbaric" and dismissed Ryan's argument that Congress must act - insisting that Sessions could unilaterally reverse the "zero tolerance" policy and return to the previous policy.
Rep. Bob Goodlatte R-Va., chairman of the Judiciary Committee, is reworking the family separation provision in the compromise bill, a GOP aide said Tuesday.
Both bills seemed to be longshots. It beefs up border security, clamps down on illegal entries and reinforces other immigration laws.
And in a speech, he strayed from his prepared remarks to express frustration about the issue and said he planned to make changes to the legislation. "We have one chance to get it right".
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"That's the law and that's what the Democrats gave us and we're willing to change it today if they want to get in and negotiate but they just don't want to negotiate".
GOP senators, including Lindsey Graham of South Carolina, Jeff Flake of Arizona and Susan Collins of ME, said they were considering legislation that would keep migrant families together; provide additional judges so detained families would face shorter waiting periods; and provide facilities for the families to stay. Rep. Mark Meadows of North Carolina, a leader of the conservative Freedom Caucus, said he has introduced a measure that "becomes a backup proposal" if others fail.
The bill, scheduled for a vote next week, also provides a path to citizenship for young undocumented immigrants but restricts legal immigration, limits asylum claims and budgets $25 billion for the construction of a border wall and other border security measures.
In the uproar over family separations, Republicans have also been crafting what they see as a legislative approach that would keep families together in detention, a provision that they've added to both bills. Florida Republican Rep. Mario Diaz-Balart told reporters that they would have "serious problems" if Trump's statement stands.
Ryan's plan has been to have the House vote next week on two bills - a hard-line measure that even its supporters say probably does not have the votes to pass the House, and a second, compromise measure that he had negotiated in hopes of gaining agreement among Republican factions.
On the Senate side, all 49 Senate Democrats have signed on to a bill from Sen. Ted Cruz, R-Texas, that would allow detained families to stay together in custody while expediting their hearings and possible deportation proceedings. John Cornyn, the No. 2 Republican in the Senate, is re-introducing his 2014 proposal created to keep families together, but speed up court dates and the deportation process for minors. When parents who come with children are arrested for jumping the border, it means at least a short-term separation while the parent goes to jail for a few days. While most have attended American schools, they have also lived under the threat of deportation.
"If you are smuggling a child, then we will prosecute you and that child will be separated from you as required by law", Sessions said in May. Remember, when I took this job three years ago, I said we'll bring stuff to the floor that may or may not pass.
He says would sign a more conservative version "or the leadership bills".
"You can let them run freely and keep the family together, or you can have quick due process at the border - adjudicating the issue immediately so that you don't have a long detention time in one of these centers", he continued. Immigration and Customs Enforcement now operates three "family residential centers" that can together accommodate about 3,330 detainees.
Sessions has defended the policy and said it will deter illegal border crossings.
"They're aiming for California - they're picking on the big gun of the resistance", said Jaime Regalado, a political science professor emeritus at California State University Los Angeles. You put them behind bars?