Senate Majority Leader Harry Reid (D-Nev.) is expected to employ a rarely used procedural tactic known as a “clay pigeon” to resume debate on the immigration bill later this week, allowing the measure’s backers to dictate the number of amendments while blocking any efforts by conservatives to slow or hijack the process, Senate aides said Friday.

At the same time, House Majority Whip James Clyburn (D-S.C.) is preparing to hold a series of “listening sessions” with Members to help shape that chamber’s version of an immigration bill, which Clyburn said he hoped would move forward regardless of whether the Senate bill passes.

In the Senate, Reid’s maneuver will allow him to add a package of supplemental spending items aimed at funding border security efforts already under way, an inducement to gain support from wavering Republicans.

According to a Democratic aide familiar with the issue, Reid is “likely” to use the clay pigeon tactic, though the source cautioned that could change between now and Thursday afternoon, when debate is expected to resume.

To use the tactic, Reid will have to bring a new bill to the floor — likely the existing bill with the new package of border spending measures — and then offer the first amendment to the measure. Reid would then split that amendment into as many as 22 separate pieces, each of which would require a separate roll-call vote, and “fill the tree,” thus blocking any further amendments.

By doing so, Reid would hold control of debate on the bill and could use a simple objection to halt any effort by GOP Sens. John Cornyn (Texas), Jeff Sessions (Ala.), Tom Coburn (Okla.) or Jim DeMint (S.C.) from offering their own changes to the bill.

Ironically, the procedural tactic — which has been used only sparingly in the history of the Senate — was resuscitated in 2006 by Coburn, who used it to force a number of votes on changes to last year’s war supplemental package as part of his broader crusade against earmarks.

DeMint spokesman Wesley Denton warned that using the tactic could come back to haunt Reid in the future. “If Sen. Reid uses the clay pigeon he’s endorsing a multiple amendment strategy and setting a precedent. He can expect Republicans to use it in the future,” Denton said.

While a final list of allowed amendments was not available at press time, GOP and Democratic aides said Republicans would be given up to 12 votes while Democrats would be given 10. Under the agreement to bring the bill back to the floor cut by Reid and Minority Leader Mitch McConnell (R-Ky.) last week, all sponsors of amendments are expected to vote to proceed to the bill. Additionally, with members of the “Grand Bargain” voting as a swing bloc, no amendments will succeed that substantively could change the bill.

With the outcome of the votes predetermined, DeMint and other conservatives have attacked their leadership, calling the process “rigged” and an unfair abrogation of the minority’s rights.

Although the clay pigeon maneuver should allow the bill to move off the Senate floor, it remains uncertain if it will ever make it to a formal conference. DeMint is expected to object to the naming of conferees on the bill, which could force Reid to use other procedural tactics to finish the bill in the future.

“Ted Kennedy [D-Mass.] has sold us another bill of goods and I don’t trust him to make even more changes to it behind closed doors in a conference with the House,” DeMint said.

A Democratic leadership aide declined to comment on how Reid would handle appointing conferees at this point. “We’re a long ways from there. Let’s drop the posturing for now and work together,” the aide said.

Across the Capitol, Clyburn will convene a series of meetings with rank-and-file Democrats to discuss immigration reform.

“I want our Caucus to delve into this and give us the benefit of their thinking,” Clyburn said in a Friday interview.

According to a memorandum distributed to Members on Friday afternoon, lawmakers are scheduled to meet in 90-minute sessions organized by geographical regions. The sessions, slated this week and next week, will be led by Clyburn along with Rep. Xavier Becerra (D-Calif.), who serves as Assistant to the Speaker.

“If [comprehensive immigration reform ] is considered in the House this session, our goal is to consider a bill that is the product of an open process and a deliberative Caucus-wide conversation,” the memo states. It later adds: “These sessions are to be frank, candid discussions that allow all Members to express their priorities for a CIR bill.”

In a separate interview, Becerra said the sessions were proposed during a recent leadership meeting as House leaders discussed how to pursue the measure in their chamber following the Senate’s failed vote to cut off debate on its version of the legislation.

“We decided what we wanted to do was to talk to, but more importantly, listen to the Members in our Caucus,” Becerra said.

Reps. Zoe Lofgren (Calif.) and Luis Gutierrez (Ill.), who have led Democratic efforts on immigration reform, also will attend the sessions to brief lawmakers on their progress.

“They’re going to come up with good legislation,” Clyburn said of current Democratic work on the reform bill. “The only problem I see is for us to sufficiently get all the elements in our Caucus to buy into the process, to feel comfortable with the process.”

He later added: “What we’re trying to do is create a climate in which we can get this [reform] done.”

In addition, the South Carolina lawmaker said that in changing the context of the debate — noting that arguments over the Senate bill have been dominated by discussions over “amnesty” provisions — he hopes the reform legislation also will gain support from Republican lawmakers, who Democrats have acknowledged will be necessary to pass any expected measure.

“My goal is still to create an atmosphere that would allow us to have a comprehensive immigration reform bill with 70 to 75 Republicans” voting for the bill, Clyburn said. He added that a recent estimate of Republican support has stood at about 30 lawmakers in the House, approximately the same number as there are Democrats expected to defect on the legislation. “I really believe, sincerely, that we can get a truly bipartisan bill,” he said.

Clyburn suggested that the discussion could even produce a final bill significantly different from the package now being proposed in the Senate, perhaps as a series of smaller measures to address areas such as border security.

“You can have comprehensive immigration reform phase in over time,” Clyburn said. “It may be we need to do this in stages.”

Even if the Senate fails again to pass a final bill, Clyburn — who once headed South Carolina’s Farm Workers Commission in the late 1960s and early 1970s — said the House will still move ahead with its plans.

“Irrespective of what the Senate may or may not do, we have a 21-member Congressional Hispanic Caucus over here, and I think it’s incumbent upon us … to give them as much hope as much respect, as we would expect them to give any other group,” he said.