House Republican leaders expressed confidence Monday that they would round up the votes to pass a border bill before Congress adjourns for its August recess at week’s end.

Members of incoming House Majority Whip Steve Scalise's team of deputy whips said legislative language would be presented to rank-and-file GOP members Tuesday morning during a regularly scheduled closed-door conference meeting.

The legislation was not yet finalized Monday evening, but the bill was expected to cost less than $1 billion and include a collection of recommendations made by the House GOP border working group.

“I think it looks very positive,” said Rep. Kristi Noem, R-S.D., after emerging from a meeting of senior House Republican leaders.

Thousands of unaccompanied minors from Central America have streamed across the southern border with Mexico in recent months. The children were sent by their parents under the belief that the U.S. government will allow them to remain here indefinitely.

Border authorities have been overwhelmed, and President Obama's administration has considered housing and schooling the children in local communities across the country.

The Republican package would seek to beef up border security to stem the tide of border crossing, speed up the legal processing of the unaccompanied minors to facilitate deportations and provide humanitarian assistance to the children already here.

The bill also would amend a 2008 human trafficking law to discourage future illegal immigration by minors. Republican sources said the legislation would cost about $600 million, and be fully offset by using unspent funds from other programs.

Rep. Matt Salmon, hardly a guaranteed “yes” vote for House GOP leaders on politically charged legislation, said he is pleased with how the package is coming together. The Arizona Republican was a member of the border working group assembled by House Speaker John Boehner, R-Ohio.

“It’s been scaled down a bit, both in content and in cost, and I think it goes a long way toward actually fixing the problem,” Salmon said.

Whipping the border bill has fallen to Scalise, who officially assumes the position of majority whip on Wednesday. The Louisianan has been handling his new duties for some days, and counting votes for the border bill is the first big test for the new No. 3 ranking House Republican and his whip team.

House Democrats are unlikely to vote for the House GOP border bill in large numbers, given disagreements they have over key policies it is expected to contain.

In particular, House Republicans want to amend a 2008 human trafficking prevention law that would make it easier to deport unaccompanied minors from Central America who illegally enter the United States.

Over the past few years, House Republican leaders have been notorious for failing to assemble 218 GOP votes for controversial measures that have minimal Democratic support. But Republican leaders are unusually optimistic and believe there is momentum among their members to address the border crisis before Congress leaves town for its five-week summer break.

“We’re going to bring legislation to deal with and solve the crisis at the border,” Scalise told reporters Monday evening. “We’re going to act — the House will act — and pass a bill to solve the problem.”

Republicans argue that a 2008 law intended to curb child trafficking has actually put these Central American children at risk by encouraging this mass migration. The law requires children to receive a legal hearing to determine whether they’re at risk and prevents them from being sent back to a dangerous situation.

Obama and congressional Democrats initially joined with Republicans in supporting a change to the law, which would require that Central American children be treated the same as those from Mexico and be deported immediately.

They later backed off after pressure from a House caucus of Hispanic Democrats and left-of-center immigration activists.