Last Thursday, the House voted to defund President Obama's orders that allow officials to focus deportation efforts on illegal immigrants who have been convicted of crimes. Reid said the vote proved the need for Congress to pass comprehensive immigration reform.

On Tuesday, the Senate will vote on whether to proceed to the Border Security, Economic Opportunity and Immigration Modernization Act, and will continue work on the legislation through June.

The bipartisan group of eight senators, known as the Gang of Eight, introduced S. 744, which would create a pathway to citizenship for illegal immigrants already in the country, toughen border security, create a guest-worker program and boost high-skilled immigration.

Reid said the bill is the “best chance” the Senate has had to tackle immigration issues in years. The last attempt, in 2007, failed.

“Over the next three weeks, senators will propose a number of ideas to make the legislation better,” Reid said. “Some will offer ideas to make it worse, but those suggestions must preserve the heart of the bill. ... The current system is broke. We can all agree on the need for action.”

Some Republicans have complained that the legislation is being rushed through and that it would provide amnesty for illegal residents before strengthening border enforcement.