(CNN) - Following meeting with President Barack Obama on Tuesday, two of the lead senators on a bipartisan effort to introduce immigration reform expressed confidence about their bill.
"We're feeling very good about this. Things are moving in a very, very good way and the president's support of our proposal, even though he wouldn't fully agree with it, is sort of just the right place to be," Sen. Chuck Schumer, D-New York, told reporters at the White House.
The bill was scheduled to be introduced during a news conference Tuesday, but the event was postponed with the nation still grappling over events surrounding Monday's deadly Boston Marathon bombing.
Schumer was joined by Sen. John McCain, R-Arizona. The two longtime senators are part of the "Gang of Eight," a group made up of four Republicans and four Democrats who've been working on a reform package they intend to file with the Senate late Tuesday night.
The bill offers a pathway to citizenship for the 11 million undocumented immigrants through a 13-year process that requires workers to pay a fine and back taxes, as well as pass a background check.
All of that, however, remains contingent on three "triggers," which Sen. Marco Rubio, R-Florida, described Sunday.
They include forming an "e-verify" system for employers to check the legal status of workers; tracking immigrants entering and leaving the country, and bolstering border security, which Rubio, one of the "Gang of Eight," specified would "include fencing."
The trigger system is the main difference between the Senate proposal and that of the president.
"The president, for instance, didn't believe in a trigger. We did. But we created a trigger that's achievable and specific, so it can't be used as an excuse not to provide a path to citizenship," Schumer said Tuesday.
Obama acknowledged the difference in a statement after his meeting with the two senators–but praised the bill, nonetheless.
"This bill is clearly a compromise, and no one will get everything they wanted, including me. But it is largely consistent with the principles that I have repeatedly laid out for comprehensive reform," he said, urging the Senate to act "quickly."
Schumer credited the president for giving the senators "space" to come up with their agreement.
After filing the bill Tuesday night, there will be Senate Judiciary Committee hearings on Friday and Monday, Schumer said. Ultimately, they hope to have the bill on the Senate floor in late May or early June, he added.
The bill marks the biggest movement towards immigration reform since 2007, when a gridlocked Congress failed to pass a bill backed by President George W. Bush. McCain said he doubts the same will happen again as the "attitude of the American people has changed since 2007."
According to a CNN/ORC International survey released Tuesday, 84% of the public backs a program that would allow undocumented workers to stay in the United States and apply for citizenship if they have been in the country for several years, have a job, and pay back taxes.
"The president also believes this is the beginning of a process, not the end," McCain said, adding he's "confident at the end of the day we will have a bill on the president's desk."
– CNN's Paul Steinhauser and Kevin Liptak contributed to this report.