House Democratic leaders on Tuesday unveiled a set of changes to a $4.5 billion package to address the flow of migrants at the southern border in an effort to win over skeptical progressive and Hispanic lawmakers.

Speaker Nancy Pelosi Nancy PelosiPelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline Trump signs largely symbolic pre-existing conditions order amid lawsuit MORE (D-Calif.) and Democratic leaders met with members of the Progressive and Hispanic caucuses late into the night on Monday to win over their support to pass the legislation, which the House is expected to consider on Tuesday.

But by mid-afternoon Tuesday, Democratic leaders had yet to formally schedule a vote on the legislation as they sought to lock down the votes and finish drafting the legislative text.

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The changes unveiled by the House Appropriations Committee include requiring Customs and Border Protection (CBP) to establish health standards for children and adults in custody, including for nutrition and hygiene.

They would also require the Department of Homeland Security to submit a plan to ensure that all migrants have access to translation services. In addition, they would limit the amount of time that unaccompanied migrant children can spend at an arrival shelter unless the Department of Health and Human Services notifies Congress that there isn't enough space at licensed facilities to ensure a transfer to a state-licensed facility.

Pelosi noted that the legislation is a funding measure, not an immigration reform bill, emphasizing the importance of getting the money to the border to deal with the crisis as the first step of a longer debate.

"It’s an appropriations bill to meet the needs of our children. ... I said to the members, ‘We have to have a country where every child knows that they are in their parents’ arms, literally or figuratively,'" Pelosi said.

House Republicans are largely expected to side with the White House and vote against the package, given their opposition to provisions that establish more restrictions for the migrant detention facilities. The White House issued a veto threat against the House bill, calling it a "partisan bill that underfunds necessary accounts and seeks to take advantage of the current crisis by inserting policy provisions that would make our country less safe."

Rep. Henry Cuellar (D-Texas), a member of the House Appropriations Committee who represents a district along the southern border, described the changes as "guardrails" designed to ensure that migrant children are protected.

He expressed confidence that the legislation would pass later Tuesday, although some liberals would likely still oppose it.

House Budget Committee Chairman John Yarmuth John Allen YarmuthPelosi, Democrats unveil bills to rein in alleged White House abuses of power GOP, White House struggle to unite behind COVID-19 relief House seeks ways to honor John Lewis MORE (D-Ky.) also predicted passage: “If we failed to do it, it would be seen as a victory for Trump.”

House Majority Leader Steny Hoyer Steny Hamilton HoyerOn The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline Vulnerable Democrats tell Pelosi COVID-19 compromise 'essential' Anxious Democrats amp up pressure for vote on COVID-19 aid MORE (D-Md.) also predicted it would pass: "I certainly expect it to."

By mid-afternoon, lawmakers were more circumspect about the timing.

When asked if she still expected a vote later Tuesday, House Appropriations Committee Chairwoman Nita Lowey Nita Sue LoweyTop House Democrats call for watchdog probe into Pompeo's Jerusalem speech With Biden, advocates sense momentum for lifting abortion funding ban Progressives look to flex their muscle in next Congress after primary wins MORE (D-N.Y.) replied, "I hope so."

Rep. Lucille Roybal-Allard Lucille Roybal-AllardHispanic Caucus asks for Department of Labor meeting on COVID in meatpacking plants Democrats may bring DHS bill to House floor Texas Democrat proposes legislation requiring masks in federal facilities MORE (D-Calif.), who leads the Appropriations subcommittee overseeing the Department of Homeland Security, said it's "very close."

Yet multiple Hispanic and progressive lawmakers said they were inclined to vote for the legislation despite their remaining reservations.

"I don't have any trust or faith that this administration is going to follow through," said Rep. Raul Grijalva (D-Ariz.) "I'm voting yes because of the humanitarian relief, period."

When asked if it was fair to say he was "holding his nose" on this vote, Grijalva replied: "More than fair."

Rep. Raul Ruiz Raul RuizHispanic caucus report takes stock of accomplishments with eye toward 2021 Jon Stewart urges Congress to help veterans exposed to burn pits House Democrat who's a physician calls on Trump to 'man up' and wear mask MORE (D-Calif.) also said that he was inclined to vote for the bill even though he doesn't think the set of changes unveiled by Democratic leaders earlier Tuesday goes far enough.

Ruiz advocated for his own bill, which would require CBP to conduct initial health screenings on detainees and directly order the agency to ensure migrants have access to water, toilets and personal hygiene products, rather than asking the agency to come up with standards.

"They're going to say, 'We already have standards,'" Ruiz said of CBP.

At the same time, Ruiz acknowledged, "The well has run dry. So at some level, you gotta put water in the well. But it's not going to change behavior. So it's a desperate bill for a desperate situation."

Lawmakers are scrambling to approve the border funding as soon as possible to ensure the Office of Refugee Resettlement, which is operated by the Department of Health and Human Services, doesn't run out of funding in the coming weeks.

The Senate is also considering its own competing $4.5 billion package this week, although it is bipartisan. House Democrats are advancing their own version because they didn't think the Senate bill went far enough to establish standards for migrants held in detention.

Among other provisions, the Senate bill includes funding for Immigration and Customs Enforcement (ICE) officers for overtime and back pay, while the House version does not.

The House measure also would require the Department of Health and Human Services to report to Congress within 24 hours if an unaccompanied migrant child dies while in the government's custody. In addition, it would allot a somewhat shorter time frame for facilities that hold migrant children to meet existing standards for humane conditions.

—Updated at 2:39 p.m.