The Senate agreed Monday to debate an immigration overhaul bill that would put millions of illegal immigrants on a path to eventual citizenship.

Sen. Majority Leader Harry Reid, D-Nev., and Senate Republican Leader Mitch McConnell, R-Ky., also agreed they will not vote on the bill by the end of this week, as was the original idea.

"There just simply is not enough time on this massive, massively important piece of legislation to do it all on Tuesday, Wednesday, Thursday and Friday," Reid said on the Senate floor, adding that the country and the Senate "deserve" more time be spent on the issue.

"The immigration system in our country is broken and needs fixing," Reid said.

The Senate, voting 69-23 on a motion to allow the debate to move forward, will debate the bill for the rest of the week and then pick it up again after the weeklong Memorial Day recess.

Sen. Orrin Hatch, R-Utah, and Sen. Bob Bennett, R-Utah, both voted in favor of the motion. This does not mean they voted in favor of the pending immigration bill but just that they agreed debate should move ahead.

"I want an immigration bill, but I want to make sure it's going to work," Hatch said in a statement. "This is a very big, complex bill, and I'm still reviewing it very carefully."

Timothy Wheelwright, past chairman of the Utah chapter of the American Immigration Lawyers Association, expressed concern that the bill could be rushed through the legislative process on the Senate floor. Typically, such major bills go through a more in-depth vetting process before such debates.

"Let's make sure that what we're getting is a system that will be workable, and predictable, not only for foreign workers, but more importantly, for U.S. employers and citizens and residents of the United States who have a stake in it," Wheelwright said.

After drawing criticism from several angles, the controversial bill will likely be amended before any final Senate vote.

As written, it would create a new four-year, renewable "Z visa," which would allow undocumented immigrants, after paying fees and a $5,000 fine, to get on track for permanent residency, which could take between eight and 13 years. Heads of households would have to return to their home countries first and must have entered the country illegally before Jan. 1, 2007, to qualify.

Activists against illegal immigration have criticized the deal as an "amnesty" and called inadequate its bolstered border security and employment verification system to ensure only legal workers get jobs.