Senate supporters still must fend off opponents' "poison pill" amendments designed to nothing more than scuttle the Border Security, Economic Opportunity and Immigration Modernization Act. However, Senate leaders and vote-counters expressed confidence the bill would pass with 60 votes, and possibly 70, before the July 4 recess.
The day the Senate began discussing the bill developed by the "gang of eight" senators -- four Republicans and four Democrats -- that would, among other things, provide a road map to citizenship for the nearly 11 million undocumented workers already in the United States and enhance border security, President Obama urged the Senate to "do the right thing" and pass the bill.
He urged those listening to his plea to contact their senators and tell them, "Don't kick this problem down the road. Come together, work together, do your job, not only to fix this broken immigration system once and for all, but to leave something better for all the generations to come, to make sure we continue to be a nation of laws and a nation of immigrants."
Obama also recognized the months of work the Gang of Eight did to get the legislation ready for consideration in the Judiciary Committee and the bipartisan passage of "more than 100 amendments."
But, for people who say the immigration system must be reformed, "there's no good reason to stand in the way of this bill," Obama said. "A lot of people, Democrats and Republicans, have done a lot of good work on this bill."
The Senate's first full vote was to stave off a filibuster, an overwhelming 82 yeas to 15 nays. All 15 senators voting to block debate were Republicans who have criticized the bill: John Barrasso of Wyoming, John Boozman of Arkansas, Michael Crapo of Idaho, Ted Cruz of Texas, Michael Enzi of Wyoming, Charles Grassley of Iowa, James Inhofe of Oklahoma, Mark Kirk of Illinois, Mike Lee of Utah, Jim Risch of Idaho, Pat Roberts of Kansas, Tim Scott of South Carolina, Jeff Sessions of Alabama, Richard Shelby of Alabama and David Vitter of Louisiana.
Senate Majority Leader Harry Reid, D-Nev., has said he expects several weeks of deliberation before taking final votes before the Independence Day break.
While House members say they, too, want to reform the nation's immigration laws, some have said they would prefer to do it in smaller chunks rather than one sweeping bill.
House Judiciary Committee Chairman Bob Goodlatte, R-Va., told The Hill in a recent interview the panel would vote on several immigration bills that address the issue in a piecemeal approach, rather than the comprehensive manner of the Senate bill.
Goodlatte was awaiting a bipartisan group of House members to nail down its comprehensive legislation.
"We think it's better to do it by a step-by-step approach," he said on "Fox News Sunday." At the same time, he said he would not rule out that the final measure would be a single piece of legislation.
House Speaker John Boehner, R-Ohio, told ABC News some aspects of the Senate bill were troubling.
"I have real concerns about the Senate bill," Boehner said. "Especially in the area of border security and internal enforcement of this system. I'm concerned it doesn't go far enough."
Asked whether he was prepared to sign on to a bill that has a path to citizenship for those already in the country illegally, Boehner said: "What I've tried to do over the course of the last six months is to create an environment in the House where members from both parties can continue to work together. And I would expect that the House bill will be to the right of where the Senate is."
Boehner said immigration reform is "probably" at the top of the most important things to get done this year.
"I think by the end of the year, we could have a bill," Boehner said.
There's a lot of political skin in this game -- including positioning in the 2014 midterm elections for senators of both parties certain to face ramifications among their constituents.
Of the 15 senators Roll Call singled out as the ones to watch, four make up two states' delegations: Mitch McConnell and Rand Paul of Kentucky and John Cornyn and Cruz of Texas. Compounding a sticky situation is the fact that McConnell and Cornyn are the No. 1 and 2 Republicans in the Senate, while Cruz and Paul are two leading conservative voices who have established themselves as being burrs in leadership's side in their brief tenures.
But Roll Call noted three Democrats -- all up for re-election and all considered vulnerable -- are the ones subject to the most scrutiny: Sens. Mark Pryor of Arkansas, Mary Landrieu of Louisiana and Kay Hagan of North Carolina, all from states Obama lost in 2012. Pryor and Landrieu voted against the 2007 immigration bill. Pryor and Hagan were among the five Democrats who voted against the DREAM Act in 2010.
Sen. Lindsey Graham, R-S.C., is the only Gang of Eight member up for re-election next year and so far has avoided a serious threat from the right, but that could change, Roll Call said.
However, Graham's recent remarks indicate he's more concerned about how his party fares in the next presidential election. Graham told reporters if the bill falls apart and Republicans are blamed, "we're toast in 2016."
Speaking of elections, GOP strategists say the party must support a plan that includes a path to citizenship -- maybe hold their noses as they do -- to level the playing field with Democrats next year in competing for Hispanic voters, the fastest growing bloc of the national electorate.
That, strategists told The Hill, would be difficult if senior GOP leaders vote against reform, giving Democrats explosive talking points.
But some GOP pundits say immigration reform is politically necessary by 2016, not the 2014 midterms.
NBC News and Roll Call pegged Sen. Marco Rubio of Florida, a Gang of Eight member who wowed the Republican National Convention and may have thoughts of running for a higher office, as a man under a microscope.
Rubio has indicated he'll need stronger border security amendments to support the bill -- and bring along more conservative votes.
"We are willing to toughen up border -- many of our colleagues feel that's important -- but without forsaking our principles," Sen. Charles Schumer, D-N.Y., and a member of the bipartisan group.
He told The New York Times border security demands must be reasonable "so that if, God forbid, there's a president in 2017 who hates immigration reform, it will still go forward."
And those who may try to draw comparisons between immigration reform and healthcare reform may want to think twice, strategists told NBC News.
Sen. Mike Lee, R-Utah, and other opponents have been trying to portray the immigration bill as the sibling of the Affordable Care Act, hoping conservative distaste for "Obamacare" will envelope the president's next attempt at legislation that would help define his presidency.
"There is a physical similarity but not a fiscal similarity," said Michael Tanner, a senior fellow at the libertarian think tank Cato Institute. "This is another giant bill with all sorts of obscure definitions and passages."
But budget-wise, they're really different, Tanner told NBC News.
"Obamacare's going to cost money, and we believe that it's going to slow economic growth," he said. "The immigration bill is actually good for the economy."