Folks, including President Obama, want it brought back to the fore.
Rallies for immigration reform were conducted across the nation as a way to urge Congress to pass reform measures.
The day after Congress approved a bill that reopened government and avoided default, Obama said sweeping immigration reform should be acted on before the end of the year.
"We should finish the job of fixing our broken immigration system. There's already a broad coalition across America that's behind this effort of comprehensive immigration reform, from business leaders to faith leaders to law enforcement," Obama said.
"In fact, the Senate has already passed a bill with strong bipartisan support that would make the biggest commitment to border security in our history, would modernize our legal immigration system, make sure everyone plays by the same rules, make sure that folks [who] came here illegally have to pay a fine, pay back taxes, meet their responsibilities," he said.
If the Senate bill becomes law, economists estimate the U.S. economy would be 5 percent larger two decades from now -- $1.4 trillion in new economic growth, Obama said.
"The majority of Americans think this is the right thing to do. And it's sitting there waiting for the House to pass it," Obama said.
If the Republican-led House "has ideas on how to improve the Senate bill, let's hear them," Obama said. "Let's start the negotiations. But let's not leave this problem to keep festering for another year or two years or three years. This can and should get done by the end of this year."
While the Senate bill offers comprehensive reform, House leaders have said they would move incrementally.
Earlier in October, House Democrats introduced their version of an immigration bill to try to spark Republican action, The Hill reported. The House minority's bill basically mirrors the Senate measure sans some border security provisions added to win Senate Republican votes.
House Judiciary Committee Chairman Bob Goodlatte, R-Va., told USA Today the measure was "basically the Senate bill."
And, he said, "I strongly oppose the Senate bill."
Democrats said they believe the Republicans' piecemeal approach is an attempt to beef up border security and employment verification measures and not provide a pathway to citizenship for workers in the United States illegally.
Many Republicans, especially those from the more conservative wing, don't want to include a pathway to citizenship for the approximately 11 million undocumented workers already in the United States.
Heritage Action for America, the advocacy arm of the Heritage Foundation, also opposes a comprehensive immigration reform bill and a path to citizenship, the Milwaukee Journal Sentinel said.
"Even before the recent crises, there was a willful ignorance of history and this idea that something would fly through," said Dan Holler, Heritage Action's communications director, noting his organization favors separate immigration bills dealing with border security and enforcement first.
"Right now, with a path to citizenship, I would say immigration reform absolutely will not pass," he said.
At a march in Washington Oct. 8, thousands of people rallied -- and 200, including several members of Congress, were arrested -- making the case for comprehensive immigration reform. Last week, 300 small groups from evangelical organizations in 30 states began nine days of prayer for immigration reform.
The clock is ticking, immigration reform advocates told the Journal Sentinel.
"The biggest issue is the calendar," said Darryl Morin, Midwest vice president for the League of United Latin American Citizens. "It's important for everyone to keep up the pressure on Congress and for everyone to remain engaged, but we're running out of time. We're not giving up, but if it doesn't happen in the fall, it could happen in the spring."
Marquette University law professor Ed Fallone, who specializes in immigration law, isn't optimistic.
"These legislative overhauls, especially big bills, need a sense of momentum behind them," he told the Journal Sentinel. "And any bill that will require bipartisanship has to happen at the right time on the calendar, so that it's not too close to the next election cycle. I do think we're starting to get close to the end of that window."
During a Chicago pro-immigration reform rally Oct. 12, a gathering of labor groups, community organizations and faith leaders organized the march numbering as many as 6,000 people carrying signs, chanting, banging drums and blowing horns, the Chicago Tribune reported.
"I thought I was a citizen because this is all I know," said Nestor Rivera, 22, a Chicago resident who said he came to this country when he was only a year old. Rivera said he has tried to become a citizen since high school, but the process has been arduous.
"It gives me hope," he said of the pro-reform march. "Things like this are getting to the government."
One of the Chicago rally organizers said October was a critical month.
"We want to continue the pressure to ensure they do pass immigration reform," Monica Trevino, spokeswoman for the Illinois Coalition for Immigrant and Refugee Rights, told the Tribune.
Immigration advocates have declared October a month of ramping up pressure for a comprehensive immigration bill, saying they fear that momentum has stalled since June when the Senate passed its bill that, among other things, includes a 13-year path to citizenship for most of the nation's 11 million undocumented immigrants.
Proponents of the Senate bill say they're concerned the government shutdown and the acrimonious atmosphere on Capitol Hill over the budget and debt ceiling will leave little time for lawmakers to focus on immigration, The Washington Post reported.
"It's going to be extremely tough to get comprehensive immigration reform, but it's not impossible," said Terry O'Sullivan, general president of the Laborers' International Union of North America, which has many immigrant workers on its member roles.
"I think there is a sense of urgency. If we don't pass something now, we won't get a vote until after the next election," said the Rev. Gay Jennings, president of the House of Deputies of the Episcopal Church and the mother of an adopted son from Colombia.
Julian Bond, a major figure in the civil rights movement in the 1960s, said at a Washington rally "immigrant rights are civil rights."
"Immigration reform must come," he said during the rally on the National Mall, which was closed because of the partial government shutdown that began Oct. 1. "It will come."