But the House refuses to debate the Senate bill, with the Republican majority deciding last week to push their own piecemeal legislation. None of those proposals so far deal with the broad legalization of the undocumented.
Utah's three Republican House members agreed with the move for smaller proposals that will focus first on border security, and two of them Reps. Jason Chaffetz and Chris Stewart have said they oppose plans that offer amnesty to immigrants who illegally crossed the border or overstayed a visa.
Rep. Rob Bishop, R-Utah, and Rep. Jim Matheson, D-Utah, have not made such definitive statements on the issue, though they also haven't supported the Senate's path to citizenship, which would take at least 13 years.
Hatch was one of 14 Republicans who did back that plan, saying it ends the current "de facto amnesty" for unauthorized immigrants by requiring them to register with the government, pay a fine and start paying taxes.
The rift has caused many in the political world, including people like Stewart, to take a pessimistic view that Congress will pass a new immigration law soon.
Hatch isn't one of them. He believes that the Republican House could offer proposals to strengthen the Senate bill and that a conference committee of the two bodies could craft a plan that could ultimately become law.
"I do think that our House members are going to take this as a very serious challenge, and quite frankly I'm counting on them," he said on the program. "Let me tell you something, I'm counting on the House. I'm counting on the House making [the Senate bill] even better, I'm counting on the House that we can't just continue on with this de facto amnesty."
This Week host George Stephanopoulos also asked Hatch, who appeared on a panel with three other members of Congress, about the George Zimmerman trial, which ended in an acquittal on Saturday.
Hatch, like other panelists, encouraged a broader discussion of race relations stemming from the case where Zimmerman shot and killed Trayvon Martin, but he agreed with the jury's verdict in the self-defense case.
"There was plenty of reasonable doubt there," said Hatch, an attorney and a member of the Senate Judiciary Committee. "At least from all I watched, it seems to me that it was an accurate verdict."