Republican leaders have tried to persuade members to hop on board. Led by Boehner, GOP leaders issued a set of immigration principles last January, for instance, drawing a negative reaction from the caucus and the subject was dropped.

Boehner also has asserted the House won’t get behind any immigration measure unless it trusts President Obama, a firm reform proponent, to enforce the law. Over the past months the White House has used discretion in enforcing immigration policy. In response, Obama has delayed a planned review of deportation policy until the end of the summer – a move that has drawn criticism from supporters and opponents.

Reform supporters are pushing for consideration of House Resolution 15, a bill similar to the bipartisan reform legislation that passed the Senate in 2013. That measure offers illegal immigrants who have resided in the U.S. since Dec. 13, 2011, an opportunity to seek provisional legal status that allows them to work but renders them ineligible for federal benefits. They must pay a penalty, taxes and a processing fee and can only apply for permanent status after 10 years. A new visa program for low-skilled workers would also be developed.

It also hikes border patrol ranks by 20,000 – almost doubling the contingent at a cost of $30 billion — and adds 350 miles of border fencing. It spends $4.5 billion on technical innovations intended to provide security personnel with full situational awareness along the southern border. And it implements an entry-exit visa program to keep tabs on visitors who overextend their stay as well as the so-called e-verify program to make employers aware of a potential worker’s immigration status.

But Boehner and other Republicans who have expressed a willingness to consider the issue are more apt to reject a huge measure like HR 15 in favor of a series of individual bills that address different aspects of the immigration debate. That likely would slow the process further and make it an unlikely topic for the 113th Congress since the bills would have to be introduced, marked up and passed and then sent to the Senate where they are likely to end up in conference.

Obama has indicated he may take executive action if Congress fails to act. The president could move to restrict deportations, expand work permit opportunities and even reduce the prosecutions of those arrested for illegal entry.

Gutierrez asserted that Latino voters are “repelled” by GOP inaction, maintaining that a “loud but small contingent of immigration opponents have backed the Republican Party into a corner they do not have the courage to break out of.”

“Even with a majority of Republican voters supporting immigration reform and a majority of Tea Party voters in support, the positions Republican candidates feel they must take in order to win over their base make them unelectable when they face the American people in the general election,” he said.

Latino voters will view 2014 as “the year it all slipped away,” Gutierrez said, unless the House acts soon.

“With or without immigration reform, Latino voters are a force that is growing faster than Republicans can withstand — and are tilting more towards the Democrats with each day Republicans stand in the way of stopping deportations that are breaking up Latino families,” he said.