The measure passed its first test when the Senate voted 82-15 on the procedural motion that brings it to the floor for consideration, the Washington publication Roll Call reported.
Obama called the legislation "the best chance" in years to fix a broken immigration system.
Speaking at the White House, the president called the proposal a compromise that would ensure all businesses and workers are "playing by the same set of rules" and set tough penalties for those who didn't.
The bill would add $6.5 billion in spending for what the president said was "the biggest commitment to border security in our nation's history." It gives employers a reliable way of checking the immigration status of each of their workers and holds employers accountable for knowingly hiring undocumented workers.
It sets out a plan for the 11 million people in the country illegally to acquire citizenship. Undocumented workers would be required to pass background checks, learn English and pay any back taxes, plus a penalty. Immigrants who had entered the country lawfully would be given priority.
Undocumented immigrants applying under the plan could not apply for citizenship for at least 13 years, Obama said,
The president said "for immigration reform to work, it must be clear from the outset that there is a pathway to citizenship."
On the other hand, the bill streamlines the process for highly skilled workers and engineers already in the United States to bring their families into the country.
Citing the numerous hearings held on immigration reform and more than 100 amendments to a bill now in Congress, the president said "there's no good reason to play procedural games" that might block "the best chance we've had in years to address this problem."
Some proposed Senate amendments threaten to split the bipartisan coalition of eight senators backing the bill and endanger the measure's chances of passage, The Wall Street Journal reported.
One expected amendment is a border-security plan from Sen. John Cornyn, R-Texas, dubbed "Results."
It would require several border-security triggers -- including a 90 percent apprehension rate of illegal crossings -- to be met before immigrants living in the United States without legal permission could transition to lawful permanent residence, or green card, status.
His amendment would also put into place an expensive biometric exit system and a nationwide electronic-verification system to make sure employers only hire workers in the country legally.
Senate Majority Leader Harry Reid, D-Nev., told Univision Cornyn's amendment was "a poison pill," also known as a "wrecking amendment," designed to destroy the bill's integrity and ruin its chance of passage.
Cornyn said on the Senate floor Monday, "The true poison pill would be the failure to take sensible measures by adopting measures like mine which are designed to solve the problem."