It’s make-or-break, do-or-die, push-comes-to-shove, every-cliche-in-the-book time for the Senate immigration bill this week, with Members jockeying for supremacy during what is likely the final week of debate on the measure. [IMGCAP(1)]

While the bipartisan bill backers say they are cautiously optimistic that it will pass the Senate this week, some of that will depend on whether GOP conservatives convince Senate Minority Leader Mitch McConnell (R-Ky.) and other Republicans to help them scuttle the bill.

Despite those efforts to delay or kill the measure, Senate Majority Leader Harry Reid (D-Nev.) expressed no uncertainty about the bill coming to a final vote this week — which would entail filing a motion to limit debate, or invoke cloture, on the bill as early as today.

“This week, we will vote on cloture and final passage of a comprehensive bill that will strengthen border security, bring the 12 million undocumented Americans out of the shadows, and keep our economy strong,” Reid said on the floor Monday.

Of course, the Senate schedule could change dramatically this week depending on the welfare of Sen. Craig Thomas (R-Wyo.), who has been battling cancer and was listed in serious condition at Bethesda Naval Hospital as of press time.

Using a “minority rights” argument to appeal to members of the Senate Republican Conference, conservatives are expected to make the case to their colleagues today that they should oppose any efforts by Reid to limit amendments or cut off debate on the bill, particularly because it did not go through the usual committee vetting process.

“The policy lunch is going to be very important” on Tuesday, said one Senate GOP aide of when conservatives will be making their pitch.

Though McConnell, like Reid, has kept his powder dry by declining to endorse or oppose the bill, he indicated Monday that he was of a mind to insist that conservatives get votes on their amendments.

“We need to have maximum opportunity for the largest number of amendments to be considered before we entertain the notion of shutting down debate on this important measure,” McConnell said on the floor Monday.

And one Senate Democratic leadership aide noted that Reid wants to “allow as many amendments as possible” before the debate ends, including voting on amendments following a cloture vote that would limit the debate to 30 hours.

Still, conservatives said they have not been comforted by McConnell’s nor Reid’s statements.

“Our leadership and our people aren’t standing up for our rights,” said one Senate GOP aide. “It’s a very frustrating process.”

The aide added that even Republicans don’t know what McConnell’s position is on the bill.

“He’s certainly not putting up a passionate fight and seems ready to just get it off [the floor] and move on to something else since it splits Republicans,” the aide said.

Meanwhile, Republican supporters of the measure say they are definitely feeling the heat from grass-roots opponents of the bill, and they’re blaming the president.

“The White House has not done us any favors,” said one senior Senate GOP aide. The aide explained that President Bush has faltered on two fronts — for failing to talk up the border security measures in the bill and for giving a speech denigrating opponents of the measure last week.

“It’s his attitude of, ‘If you’re not with me you’re totally against me and wrong,’” said the aide. “Then we’re the ones left holding the bag.”

Several GOP Senators supporting the bill — Sens. Lindsey Graham (S.C.), Johnny Isakson (Ga.) and Saxby Chambliss (Ga.) — have been booed by fellow Republicans at recent state party conventions, and protesters gathered outside the Jackson, Miss., office of Senate Minority Whip Trent Lott (R-Miss.) over the weekend.

GOP aides also complained that the White House has done little to reach out to Republicans who have been supportive of the president’s position.

But Commerce Secretary Carlos Gutierrez said in an interview Monday that he and other administration officials have been meeting with outside groups and supportive Senators, “constantly getting the message out that this is a good bill and a strong bill from the standpoint of border security” and other things.

He also defended Bush’s remarks last week that conservatives who oppose the bill don’t want to “do what’s right for America.”

“I think the president was outstanding last week,” Gutierrez said. “You could see and feel how passionately he feels about this and how important he thinks this is for the country.”

Despite general Republican disunity on immigration, GOP aides said they did not expect any Republican bill backers to defect this week, despite some tough votes on amendments from Sens. John Cornyn (R-Texas) and Jim DeMint (R-S.C.).

DeMint has said he will “fight to improve the bill, and if he can’t do that, he’ll fight to block it,” his spokesman said.

It’s unlikely DeMint will have the support of the 40 Senators necessary to sustain a filibuster, and Gutierrez predicted that the final “vote will show there is strong support for comprehensive immigration reform in the Senate.”

The bill also has come under assault from the left in the Senate, but Democratic bill supporters, led by Sen. Edward Kennedy (Mass.), have so far been able to hold the line against “poison-pill” amendments from fellow Democrats.

Even if the bill limps out of the Senate, there is little question that it will face an even tougher road in the House, where support for the measure among Members of both parties is dicier.

Like the Senate, there is no shortage of House conservatives waiting to take the first shot at the bill should it emerge from the Senate.

Conservative lawmakers are feeling a “tidal wave of anger over amnesty,” said one Republican staffer, of the bill’s provisions providing current illegal immigrants with a path to citizenship. The bill cannot have “the smell of amnesty” or it will be “dead on arrival,” the staffer predicted. “I don’t know that there is any saving it in the House at this point.”

Steven T. Dennis contributed to this report.