With his handling of the bill, committee Chairman Patrick Leahy broke the string of secret, high-level negotiations that have been the hallmark of all the major budget and tax bills preoccupying Congress since 2011.
"I think the more open and transparent the process the better," said Democratic Senator Mary Landrieu of Louisiana. She added, "It makes senators feel like...they've expressed their views. It will cut down on the partisanship, hopefully."
Angela Kelley, an immigration expert at the liberal Center for American Progress, said that the bipartisan comity struck in the Senate Judiciary Committee "matters a lot" for the bill's prospects before the full Senate.
"In some ways, the lack of drama is really different from when it (immigration legislation) was marked up in committee in 2006 and in 2007 when so much of that negotiation was happening behind closed doors. It left just such a bad taste in people's mouths that it (the bill) didn't have the juice it needed to get off the floor," Kelley said.
But the bipartisan spirit will go only so far, as the trouble among House members trying to work out a bill was demonstrating.
In addition to discord over healthcare, there also were disagreements over the future enforcement of border provisions and other security programs, such as the "E-verify" that employers will use to ensure they are hiring legal immigrants.
Republican Representative Raul Labrador of Idaho, one of the House negotiators, told reporters there is a Thursday deadline for working out an agreement among the eight lawmakers on healthcare provisions of their long-sought immigration bill.
At issue is whether newly legalized immigrants, barred from getting any government help in buying health insurance, will be able to afford to pay for their own policies.
Some Democrats fear that without any health insurance, these people could face deportation if they are bankrupted by huge medical bills. That is because at various points, they would have to demonstrate economic independence in order to maintain their legal status.
House Democratic leaders, according to congressional sources, were mulling whether any bipartisan House bill ought to be unveiled. Instead, they are wondering if there might be a better outcome for President Barack Obama and his fellow Democrats if the House simply was presented with a Senate-passed bill.
"If the Senate passes a bill...that would reflect a pretty broad, bipartisan support of that bill, and I would think that that would be a good basis for our discussion here," Representative Steny Hoyer, the second-ranking House Democrat, told reporters on Tuesday.