The House of Representatives is set to vote on a $4.5 billion aid bill for migrants at the U.S.-Mexico border Tuesday, despite dissent within the Democratic caucus and opposition from the White House.

The bill would increase protection and health services for migrant children and impose stricter rules for temporary influx shelters, but would not fund a border wall or more beds at Immigration and Customs Enforcement (ICE) detention centers.

Hispanic and progressive representatives pushed House leadership to add more protections for migrants during a meeting with House Speaker Nancy Pelosi Monday night, but some remain opposed to any bill which funds Customs and Border Protection (CBP) and ICE. Pelosi argued in a statement Sunday that the bill "does not fund the Administration's failed mass detention policy, but, instead funds effective, humane alternatives to detention with a proven track record of success."

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However, Reps. Alexandria Ocasio-Cortez, Ilhan Omar, Ayanna Pressley, and Rashida Tlaib issued a joint statement Sunday saying that they would not support this bill, which they say "gives even more money to ICE and CBP and continues to support a fundamentally cruel and broken immigration system."

The Senate will also be voting this week on similar legislation that has bipartisan support, although House Democrats argue that the Senate legislation does not provide enough protections for migrant children.

In a meeting with House Democrats Tuesday morning, Pelosi said that the bill was an appropriations bill, not an immigration bill, according to a senior Democratic aide.

"The Senate has a good bill. Our bill is much better. But if we are going to prevail we have to have a good, strong vote. You can find fault with any bill that comes down the pike, but we must respect the bill for what is does rather criticize it for what it does not," Pelosi said in the meeting. She also warned her caucus that the "president would love for this bill to go down today."

Even if the House passes its version of the bill largely along party lines and despite the opposition of some progressives, President Trump has threatened to veto the House version should it also pass the Senate. In a letter to the House Monday, White House officials complained that the House bill did not provide funding for more ICE beds, a wall or other border security measures.

"Because this bill does not provide adequate funding to meet the current crisis, and because it contains partisan provisions designed to hamstring the Administration's border enforcement efforts, the Administration opposes its passage," the letter said, according to the Associated Press.

House Republican leaders blasted Pelosi for not bringing up the border supplemental bill sooner and said she was filling it with poison pills to prevent it from passing. Minority Leader Kevin McCarthy said he would vote for the Senate bill if she brought it to the floor, but not the current House version.

"I'm calling on the speaker not to play politics, to take the Senate bill, and that could become law," McCarthy said.

The House vote comes after Mr. Trump delayed a mass deportation crackdown by two weeks. Mr. Trump tweeted over the weekend that he would give Congress time to reach an agreement on immigration.

"At the request of Democrats, I have delayed the Illegal Immigration Removal Process (Deportation) for two weeks to see if the Democrats and Republicans can get together and work out a solution to the Asylum and Loophole problems at the Southern Border," Mr. Trump wrote on Twitter Saturday afternoon. "If not, Deportations start!"

ICE was expected to target more than 2,000 families with pending deportations orders as part of the crackdown. Mr. Trump had announced the raids ahead of his 2020 re-election launch Tuesday, tweeting: "Next week ICE will begin the process of removing the millions of illegal aliens who have illicitly found their way into the United States. They will be removed as fast as they come in."