Earlier this month, President Barack Obama sought $1.8 billion in emergency funds to better take care of these minors. He also wants $1.6 billion to boost border security and add new judges and prosecutors to speed up asylum and deportation hearings.
Congress has yet to take action on Obama's request, which has become mired in the touchy politics of immigration reform.
Chaffetz, who, like most Republicans, has opposed the Democratic president's efforts at wider immigration reforms, has criticized Obama's handling of the border crisis.
"The administration," Chaffetz said, "has been telegraphing to the world that if you just step foot in the United States, we will not deport you."
His bill, like Obama's request, would increase the number of judges hearing deportation cases. But Chaffetz also wants to make it more difficult for immigrants to gain asylum by claiming a credible fear of persecution in their home country. His proposal would require prospective immigrants to offer evidence in support of their stories, a move he hopes would slow the rapid growth in such asylum claims.
"Asylums are a worthy process for some people," he said, "but it is being abused."
Chaffetz started working on this legislation months before the current crisis. He visited the Arizona-Mexico border in April 2013 and said he observed a problem with asylum and unaccompanied minors then, a year before the recent surge in minors at the crossings. In reaction to this wave, he updated his original proposal to fast-track such deportation hearings.
His legislation also would allow Border Patrol agents to access protected federal lands, borrowing from a bill previously sponsored by Rep. Rob Bishop, R-Utah.
Obama has drawn fire on the issue from all sides. While Republicans, such as Chaffetz, want faster deportations, some Democrats, including the members of the Congressional Hispanic Caucus, have called on him to show compassion to these children and allow those with relatives in the country to stay.