"It's a very long and winding road to immigration reform," said Rep. Tom Cole, an Oklahoma Republican who said it could be late this year or perhaps early in 2014 before the outcome is known. His own constituents are "very skeptical, mostly opposed," he said.
Supporters of the Senate's approach sought to rally support for its promise of citizenship for those who have lived in the United States unlawfully, a key provision alongside steps to reduce future illegal immigration.
"The Republican Party still doesn't understand the depth...of this movement and just how much the American people want comprehensive immigration reform," Rep. Luis Gutierrez, D-Ill., said on Friday. "We need to make sure they come to this understanding."
But Rep. Matt Salmon, R-Ariz., said in an interview that any bill that results in citizenship was a nonstarter. He called the approach "patently unfair" to those trying to "do it the legal way."
Within hours after the Democratic-controlled Senate approved its bill Thursday on a 68-32 vote, President Barack Obama telephoned with congratulations for several members of the bipartisan Gang of Eight who negotiated an early draft of the bill that passed.
Traveling in Africa, he also called House Speaker John Boehner, R-Ohio, and Democratic leader Nancy Pelosi of California from Africa, urging them to pass an immigration bill.
Yet not even a firm timetable has been set.
The House Republican rank and file is scheduled to hold a closed-door meeting on the issue shortly after returning from a July 4 vacation, and Boehner has said previously he hopes legislation on the topic can be passed by the end of the month. Aides also say it is possible the issue wouldn't come to the floor until the leadership had successfully resurrected a farm bill that was defeated last week.
In contrast to the all-in-one approach favored by the Senate, the House Judiciary Committee has approved a series of single-issue bills in recent days, none including a path to citizenship that Obama and Democrats have set as a top priority.
One, harshly condemned by Democrats, provides for a crackdown on immigrants living in the United States illegally. Another sets up a temporary program for farm workers to come to the United States, but without the opportunity for citizenship the Senate-passed measure includes.
A third, which drew several Democratic votes, requires establishment of a mandatory program within two years for companies to verify the legal status of their workers. The Senate bill sets a four-year phase-in, although supporters of the legislation have also signaled they are agreeable to tighter requirements. A fourth increases the number of visas for highly-skilled workers.
Rep. Zoe Lofgren, D-Calif., criticized the approach followed so far by House Republicans. "We have taken up a series of small-bore partisan bills that are in some cases bizarre," she said at a panel discussion hosted by Bloomberg Government and the National Restaurant Association. "We have not touched the whole issue of how you get 11 million people right with the law."
Also appearing on the panel, Republican Rep. Mario Diaz-Balart of Florida said the House must find a solution for the estimated 11 million immigrants now living in the United States unlawfully. "Ignoring that reality does not make it go away," he said.
Lofgren and Diaz-Balart are part of a bipartisan group that has tried to struggled unsuccessfully so far to produce legislation roughly comparable to the one drafted by the Gang of Eight in the Senate.
In their discussions to date, the lawmakers have agreed to a pathway to citizenship over 15 years, two years longer than the Senate legislation provides. Their efforts at an overall compromise have stumbled over details of a guest worker program and other issues.
The situation was far different in the Senate, where the Gang of Eight drafted legislation, shepherded it through the Senate Judiciary Committee and then helped negotiate tough border security requirements that helped swell Republican support.
As the measure was passing the Senate on Thursday, members of the Gang of Eight were urging the House to be ready to compromise.
"You may have different views on different aspects of this issue, but all of us share the same goal, and that is to take 11 million people out of the shadows, secure our borders and make sure that this is the nation of opportunity and freedom," said Sen. John McCain, R-Ariz.
The bill passed by the Senate devotes $46 billion to border security improvements, including calling for a doubling of the border patrol stationed on the U.S.-Mexico border and the completion of 700 miles of fencing. No immigrant currently in the United States illegally could qualify for a permanent resident green card until those border enhancements and others were in place.
Associated Press reporters Luis Alonso Lugo, Donna Cassata and Jim Kuhnhenn contributed to this report.