Senate proponents of a bipartisan overhaul of the nation’s immigration laws are bracing for what could be a rough recess week, planning daily press conferences and other outreach efforts in the runup to the Memorial Day break aimed at countering withering criticism aimed at the deal.

At the same time, immigrants’ rights organizations, labor unions and conservative opponents of the bill are all stepping up their attacks and hope to use the break to pressure rank-and-file Democrats and Republicans to kill the legislation.

While members of the bipartisan group, which crafted the reform deal now being debated on the Senate floor, convinced Majority Leader Harry Reid (D-Nev.) to give them an extra week following the Memorial Day recess to complete the bill, the delay also gives opponents significant time to build momentum against the deal.

In fact, GOP Sens. Lindsey Graham (S.C.), Saxby Chambliss (Ga.) and Johnny Isakson (Ga.) — who are members of the 12-person bipartisan group behind the deal — were booed during home-state events Saturday, and several aides said Tuesday their offices have been inundated with negative calls.

“Our phone’s been ringing off the hook,” one Republican aide said, adding “and none of them have been positive.”

Sen. Dianne Feinstein (D-Calif.) — a key negotiator of the deal — said Tuesday that her office has received negative feedback on the bill, though it has not yet reached a level of concern for her. “The bulk of the calls have been hostile,” Feinstein said, explaining that “In California, when you get 40,000 or 50,000 calls you know something is going on, and I’ve only gotten about 4,000 calls.”

In order to push back against what they see as a campaign of misinformation being spread about the bill, negotiators are hoping to use the next several days to tilt the public debate in their favor. Feinstein and Kyl announced Tuesday that members of the bipartisan group would hold daily press briefings, and Democratic and Republican aides have been holding daily briefings on the bill for reporters.

Similarly, Democratic Sens. Edward Kennedy (Mass.) and Ken Salazar (Colo.) Tuesday met with a group of Hispanic Christian evangelical radio broadcasters to brief them on the bill.

Supporters also are working to win over their colleagues before they return home. Salazar gave an impassioned speech about the issue during the Democrats’ weekly luncheon Tuesday, Kennedy said, in which he made the case that the Senate has a moral responsibility to address illegal immigration.

Sen. Mel Martinez (R-Fla.) helped brief Republican Senators during their luncheon and said the session went well. “I was very gratified by some of the comments,” Martinez said, adding, “the mood was positive.” Senate Republicans are scheduled to meet this morning to discuss the legislation.

Sen. Jon Kyl (R-Ariz.) also briefed House Republicans on the bill’s provisions, although Sen. Jeff Sessions (R-Ala.) — an opponent of the deal — also presented what he sees as flaws in the bill.

Martinez acknowledged that supporters will need to fight what he sees as misunderstandings of the bill’s inner workings and that the recess may give them the time to educate members and the public. “With the amount of misinformation out there, it may be helpful for the right information, the things that are in the bill, to be known,” he said.

“I think there has been a lot of misinformation that I hope will be corrected in the days to come,” Martinez added.

But aides on both sides of the aisle privately said it was unclear whether Members could successfully explain the bill during the recess given the amount of opposition to the deal. One senior Democratic aide said enough lawmakers either oppose the bill or are on the fence that opponents could easily put together a coalition of left- and right-leaning Members large enough to block the bill in the Senate, particularly if Members are bombarded with negative comments and hostility from constituents next week.

Aside from the business community, virtually all outside interest groups have expressed some level of opposition to the agreement. The AFL-CIO is working through its locals with immigrants’ rights groups and other labor organizations on protests for next week in Chicago and other major cities, and pro-immigrant activists said marches, meetings and other events are expected next week.

Cecilia Muñoz of the National Council of La Raza said while no plans had been formalized, her organization and local groups were planning to use the recess to pressure lawmakers. “I think you will see a variety of things from town hall meetings to vigils to calls and individual meetings as well. But, yes, I think that you can expect the activity around the country to be vigorous over the break … we do know that local organizations around the country are mobilizing very forcefully around these issues and I think you can expect quite a bit of activity,” Muñoz said.

Jamie Weinstein contributed to this report.