After finally reaching agreement last week on a basic immigration reform package, the small bipartisan group of Senators backing the deal will spend the next three weeks fighting to keep the bill intact amid rhetorical and legislative assaults from the right and left.

The Senate on Monday voted 69-23 to begin debate on the immigration measure, which will start in earnest today as Members begin slogging through what could be scores of amendments.

While Senate Majority Leader Harry Reid (D-Nev.) had repeatedly said he expected the bill to be done by Friday, he “reluctantly” conceded on the floor Monday evening that it would be “better if we not try to finish this bill this week.”

“When we come back the week after Memorial Day break we’re going to spend that on immigration,” Reid said.

The Democrat’s change of heart came after Minority Leader Mitch McConnell (Ky.) and other Republicans had urged him not to hold the chamber to that deadline if progress is being made on the measure.

“I think attempting to finish this bill this week would be unsuccessful,” McConnell said earlier on Monday. “This is a two-week bill.”

Democratic aides agreed it made sense for the measure to slip past the Memorial Day recess.

“I don’t expect any time agreements will be possible on this bill,” said a Democratic aide.

Following the model the Senate used to move immigration legislation off the floor last year, a core group of 12 Republican and Democratic lawmakers — including Sens. Jon Kyl (R-Ariz.), Edward Kennedy (D-Mass.), Arlen Specter (R-Pa.), Dianne Feinstein (D-Calif.), Lindsey Graham (R-S.C.), Mel Martinez (R-Fla.) and Ken Salazar (D-Colo.) — will meet each morning this week to map out a strategy for handling amendments expected to be voted on that day, Senate aides involved in the bill said Monday.

According to the Democratic aide, the lawmakers have agreed to vote as a bloc against any amendments that will substantially change the basic deal or put passage of the legislation in jeopardy.

“When we had the immigration bill on the floor last time we had a process” for the negotiators to vote together to avoid any poison pills, the aide said. “We’ll be doing the same this time,” the aide continued, adding that “there’s a commitment to make [voting] decisions jointly.”

According to aides on both sides of the aisle, lawmakers are still reviewing the bill, which was released Saturday, and the number of amendments to be offered remains unclear. At the very least, Democrats are expected to look for changes to the bill’s guest-worker provisions as well as restrictions on future legal immigration.

Republicans, meanwhile, are readying amendments to beef up enforcement of border controls and employment verification rules and the bill’s “Z Visa” provisions, which help the 12 million illegal workers in the country now enter the process for citizenship. Republicans also will look to make changes to legal appeal provisions in the bill as well as current law, aides said.

With Friday no longer the deadline for final passage, it is unclear whether the agreement can survive a full three weeks under attack from all sides. Conservatives and progressive activists already have come out against the bill, and several Republican lawmakers received hostile receptions from home audiences over the weekend.

For instance, Georgia Republican Sens. Saxby Chambliss and Johnny Isakson were booed during a state Republican Party dinner Saturday because of their involvement in the bipartisan group that negotiated the deal, while Graham also received a hostile reception at his state’s annual convention.

While none of those Members has shown any signs of defecting from the deal, rank-and-file Members could find it particularly difficult to withstand a weeklong assault from partisan organizations during next week’s recess.