They would attempt to introduce the amendments by delaying the legislative process long enough to offer the poison-pill revisions to the "Gang of Eight" proposal, the lawmakers and aides told The Washington Post.
A poison pill amendment -- also called a wrecking amendment or a killer amendment -- seeks to re-form a bill or severely change its intent so it becomes all but useless and dies.
The tactics were used successfully by Senate opponents of 2007's Comprehensive Immigration Reform Act.
That bill was never voted on, but amendment votes were held.
The new effort to kill the immigration bill would seek to exploit a perceived public divide over core components of the comprehensive legislation introduced Tuesday by the eight lawmakers, who spent months negotiating the details.
Conservative opponents have begun arguing a bill provision that lets unauthorized workers stay in the United States amounts to "amnesty." They also argue proposed new border-control steps are not strong enough and the guest-worker program would hurt American jobs at a time of high unemployment.
The Gang of Eight plans to tout the proposal in a news conference with immigration advocates, business leaders and religious groups as early as Wednesday.
But conservative critics told the Post they wanted to make sure the legislative process is not rushed.
An open process "is essential to gaining public confidence in the content of the bill," said Sen. John Cornyn, R-Texas.
Cornyn is the top GOP member on the Senate Judiciary Committee's immigration subcommittee.
"I can't see any reason to undermine confidence by trying to jam it through without adequate time for people to read it and to hear from their constituents," he said.
Sen. Chuck Grassley, R-Iowa, told the newspaper he considered the legislative speed a "serious problem."
The Senate Judiciary Committee has scheduled hearings on the immigration bill Friday and Monday.
Sen. Chuck Schumer, D-N.Y., a member of the bipartisan Gang of Eight, has said the goal is to have the Judiciary Committee open the bill for amendments in early May and get it to the Senate floor by early June.
"One thing he made clear is he wants to have an open process but he doesn't want to delay and drag this out, because that's the way bills get killed," Schumer told the Post. "That's one of the most important points he made."
In a statement, Obama said, "I urge the Senate to quickly move this bill forward and, as I told Senators Schumer and McCain, I stand willing to do whatever it takes to make sure that comprehensive immigration reform becomes a reality as soon as possible."
Sen. Marco Rubio, R-Fla., another member of the bipartisan group, told CNN's "State of the Union" Sunday he expected unspecified lawmakers would introduce poison-pill amendments to doom the measure.
"I'll oppose those if I know that's what they're for," he said.
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