The first test for the immigration bill will come in the Senate on Tuesday when a procedural vote is held to formally bring the measure before the full 100-member chamber. Supporters of the bill are expected to get the 60 votes needed to clear the hurdle.
Many amendments are expected to be debated over the next few weeks as the Senate tries to pass its bill by July 4.
Republican Senator Marco Rubio, a Cuban-American lawmaker from Florida and one of the authors of the bill, on Tuesday said he would offer an amendment to tighten English language proficiency requirements for illegal immigrants who are trying to gain permanent residency in the United States.
Representative Chris Van Hollen, a Maryland Democrat and a member of his party's House leadership team, said on CNBC that it was unclear what kind of bill the House will be able to pass this year.
"I think Speaker Boehner would like to get some kind of comprehensive immigration reform through. The question is whether or not his caucus is willing to support that effort," Van Hollen said.
Van Hollen said that last week House Republicans pushed through passage of a measure that would resume deportations of children brought to the United States illegally by their parents.
Obama acted a year ago to temporarily suspend most of those deportations, noting that the children had no control over their illegal arrival into the United States and many of them had grown up here with little or no remaining ties to their native countries.
In his remarks on Tuesday, Obama also noted that border enforcement had improved dramatically under his administration's tenure and said immigration reform could only work if undocumented individuals had a chance to become citizens.
Leaders from business, labor, the religious community, and law enforcement joined Republican and Democratic lawmakers at the White House event. (Additional reporting by Mark Felsenthal, Roberta Rampton, and Susan Heavey; Editing by Paul Simao)