JUDY WOODRUFF: Now we turn to an issue that had been expected to move through Congress this year, immigration reform, but which has instead become stalled.Ray Suarez has our report.

RAY SUAREZ: Thousands of fans cheered on Los Tigres del Norte, in English, Tigers of the North, as theMexican immigrant superstars sang about the plight of undocumented workers on the National Mall Tuesday.

RAY SUAREZ: The group's free performance was part of a daylong rally, a rally that was allowed to go forward in the face of the government shutdown because public areas like the National Mall are open forFirst Amendment-related activities, whether the government's up and running or not.The gathering was sponsored by labor groups and immigrant rights organizations. It was meant to bring attention to the drive for immigration reform.

WOMAN: In spite of my brown skin and black hair, I am American. American really means that you're an immigrant and that you left where you were at because it was a struggle and you came to America for a better future.

RAY SUAREZ: These thousands arrived on the National Mall on the heels of more than 100 weekend demonstrations around the country. Chants of "Si, se puede," "Yes, we can," were heard from Phoenix, Arizona,to a march toward the Rhode Island state capitol.The crowd wasn't large by the standards of demonstrations that have used the National Mall over the years. Supporters said the coordinated nationwide effort was meant to send a message to Congress.

ANJELICA OTERO, protester: My message is let's just make sure that we create a bill that moves people to a path to citizenship, that stops deportations and that really helps to reunite families.

RAY SUAREZ: House Democrats have introduced new comprehensive immigration reform legislation. It basically mirrors the bipartisan Senate bill passed last June, calls for a pathway to citizenship, along with heightened border security. The one hiccup, Republicans say, is, the bill is dead on arrival.

REP. TREY GOWDY, R-S.C.: We really do need to get fiscal issues behind us, because for whatever reason, we just don't seem to be able to multitask very well in this town.

RAY SUAREZ: Despite a major push by advocates after the Senate bill passed, the government shutdown and, before that, events in Syria have taken center stage since Congress returned from its summer recess.And Republican Trey Gowdy acknowledges that even before the current partisan battles, passing comprehensive reform was a long shot.

TREY GOWDY: There is a joke in the House that comprehensive is Latin for too big to read. I think theword comprehensive has a pejorative connotation in today's political world, and folks would rather -- at least from my vantage point, rather us take it issue by issue.

RAY SUAREZ: Gowdy, like most of his Republican counterparts, favors peeling off issues, like border security and work visas, one at a time, although he did leave the door open to the idea of a larger compromise bill down the road.

TREY GOWDY: So, the fact that we debate them and vote on them separately doesn't mean they will not becobbled together at some point for one vote.

MAN: Will you march with us?

RAY SUAREZ: In the meantime, Democrats are getting creative in their fight to keep up the pressure. After marching from the Mall to the U.S. Capitol Tuesday, Luis Gutierrez was one of eight members of Congress to be arrested for civil disobedience, along with more than 150 others.

REP. LUIS GUTIERREZ, D-Ill.: The intensity and the hunger and the passion for comprehensive immigration reform is not waning in the immigrant community.

RAY SUAREZ: And while Gutierrez admits immigration reform is unlikely to pass anytime soon, he insiststhat, behind the scenes, both parties are trading ideas.

LUIS GUTIERREZ: Every day, every day, there are conversations, negotiations, trading of ideas between Republicans and Democrats. Maybe it is that quiet diplomacy, without headlines, and a kind of quiet --without the kind of pressure that the fifth estate sometimes places on us for momentum and energy, that we find our own momentum and our own energy, and in the end surprise you all and say, wow, this isthe one you didn't expect.

RAY SUAREZ: For now, lawmakers are still in a fiscal deadlock. One of the few things Republicans and Democrats agree on in Washington is that an immigration debate won't begin until the shutdown and debtceiling battles end.