A Senate test vote on a new immigration reform bill garnered the 60 votes needed for lawmakers to begin debating the 1,000-page document, but Senate leaders agreed Monday to postpone finishing the bill until next month.

In a nod to opposition, Senate Majority Leader Harry Reid conceded that the Senate won't seek to complete the bill before a hoped-for Memorial Day deadline.

"It would be to the best interests of the Senate ... that we not try to finish this bill this week. I think we could, but I'm afraid the conclusion wouldn't be anything that anyone wanted," Reid, D-Nev., said.

In rare agreement, both the White House and Reid had indicated they wanted final passage of the bill to occur by Friday before the Memorial Day recess. But many others, including Minority Leader Mitch McConnell, R-Ky., have said one week is simply not long enough to discuss all the expected amendments.

The Senate was ready to get into a multi-week debate, however, voting 69-23 to proceed with amendments on the bill.

Click here to see how your senator voted on proceeding with debate on the immigration reform legislation.

Sen. Jeff Sessions, R-Ala., probably the most outspoken critic of the comprehensive immigration reform bill, offered a three-hour critique of the bill to kick off Monday's debate. Propped up next to Sessions was a giant picture of a famous scene from Schoolhouse Rock's "I'm just a bill" skit.

He criticized the backroom negotiations that gave birth to the legislation, saying "masters of the universe" ignored the proper committee approval process and instead met "in secret rooms to come up with a grand compromise."

He later said he was pleased that Reid agreed with his request to delay a final vote.

"The bill is critically important to the American people, and to railroad it through the Senate would be unthinkable. ... The recess week will provide some time for senators and the American public to become familiar with this extraordinarily complex legislation and to better understand its consequences," he said.

Even Reid took aim at a number of components of the bill, including a temporary guest worker program that sets up three two-year stints for workers provided they return to their home country for a year in between each work period. Temporary workers who bring family members are permitted only one two-year work period.

"We must not create a law that creates a permanent underclass," Reid warned.

A minimum of 400,000 work visas will be distributed to immigrants per year with a ceiling of 600,000, something that rankles many unions. To that end, Sen. Jeff Bingaman, D-N.M., will offer an amendment to reduce that number to 200,000, the same item passed overwhelmingly last year.

The centerpiece of the new legislation is a "Z-visa," to be offered to some 12 million illegals if they pay fines, learn English and return to their countries to file paperwork. That would set them on their way toward permanent residency.

Many critics of this bill have zeroed in on the Z-visa provision, calling it amnesty. Illegals already in the U.S. can obtain a Z-visa and work here indefinitely without any return to their home country for legal re-entry. The so-called "touchback" or home country return must occur only for those who seek to become U.S. citizens.

Reid declared the new point system by which immigants earn a green card "not good enough," saying that it "rips at the heart of families." Only nuclear family and 40,000 "grandparents" per year and no other extended family can come with an immigrant once that person gets a green card or once an illegal declares himself and is granted a Z-visa.

The cost of legalizing the 12 million illegal immigrants already in the country also is a concern to bill opponents.

The conservative Heritage Foundation released a report on Monday analyzing future costs of households headed by workers without a high school diploma. Data from 2004 shows that 50 percent of illegal workers fall into that category. The data also indicate that such households consume more in benefits than they pay in taxes.

"Each low-skilled immigrant household that gets amnesty costs the American taxpayers nearly $20,000 each year if we consider only the illegal aliens given amnesty." said Sen. Jim Bunning, R-Ky. "Those costs will add up to over $2 trillion — that's with a 't' — trillion over their lifetime."

Click here for more coverage in FOXNews.com's Immigration Center.

McConnell has said much of the bill's survival depends on a provision that sets triggers to be met on border security and worker documentation before moving forward on giving legal standing to illegals.

In the House, conservative lawmakers are also preparing for their own debate once the Senate passes its legislation.

Rep. Dan Lungren, R-Calif., introduced legislation he said was "an alternative to several of the large holes in the so-called Senate compromise."

Based on lessons learned following Congress' last major attempt at reform in 1986, Lungren, a major player in those negotiations and GOP floor manager of that bill, said strong enforcement is a must.

"If you promise enforcement and you don't have enforcement, forget about it. If you promise enforcement, you better do it up front. That's why the trigger mechanisms — at least the sense of a trigger mechanism in the Senate makes a great deal of sense."

However, he added, that the Senate bill "needs to be fine-tuned" and identified several key provisions that he is including in his own legislation.

Under his plan temporary workers would get to spend 10 months in the states, 2 months required back in country of origin with incentive to return for those two months.

His incentives include requiring "that FICA and the unemployment tax be withheld from the workers' wages and deposited into a trust fund. The employer contribution to FICA and the unemployment tax would be used for the purpose of administering the program. The employee contribution to FICA would be returned to the employee only upon return to his or her country of origin, and would be collected at the nearest American consulate."

According to his plan, if guest workers fail to be in their country within the period of time that they are required to be — that is, the two months out of the year that they're supposed to be there — they would forfeit the right to the money, would be ineligible for further participation in the program and would be subject to arrest and deportation if they came back to the U.S.

In answer to Z-visas, Lungren proposes creating "blue cards" that would changes the date for qualification in this class of individuals to Jan 2002; as opposed to Jan 2007 in the Senate language. Applicants would be required to pay $1,000; would not have "lawful permanent resident status," but could return home to apply for green card before returning to work in the United States while they await the green card. It would not provide for family members to immigrate with them.

"It would allow those who have been in the country for five years or more to apply for a program which would enable them to stay in the United States, to work here, to travel inside and outside the country. But the one thing it would not do would be to establish a new process for the illegal alien population to become permanent legal residents and eventually citizens," he said.

FOX News' Trish Turner and Molly Hooper and The Associated Press contributed to this report.