WASHINGTON — As a Senate committee prepares to begin voting this week on far-reaching immigration legislation, advocates are watching warily to see whether relatively tame opposition balloons into the kind of fierce resistance that killed Congress’ last attempt to overhaul the system.

Last time around, in 2007, angry calls overwhelmed the Senate switchboard and lawmakers endured raging town hall meetings and threats from incensed constituents. The legislation ultimately collapsed on the Senate floor.

“I’ve been through this battle, and it’s ugly,” said former Sen. Trent Lott, R-Miss., who supported the bill. “My phones were jammed for three weeks and I got three death threats, one of which I turned over to the FBI. So it’s rough business.”

Supporters of the immigration bill brought forward last month by a group of four Republican and four Democratic senators have been cautiously optimistic about their prospects because of factors including public support for giving citizenship to immigrants, a large and diverse coalition in support of the bill, and a growing sentiment among Republican leaders that immigration must be dealt with if they are to regain the backing of Hispanic voters.

Backers have been working hard to build alliances and strategies aimed at avoiding the mistakes of 2007, when critics largely defined the bill and some supporters ended up turning against it.

Opponents acknowledge that supporters started out better organized and mobilized than last time around, and they also anticipate that outside groups pushing the legislation — including efforts headed by New York Mayor Michael Bloomberg and Facebook founder Mark Zuckerberg — will outspend them. Supporters include large and influential groups including the U.S. Chamber of Commerce, AFL-CIO and the Catholic Church, while opponents include lesser-known think tanks or advocacy organizations such as NumbersUSA, the Federation for American Immigration Reform and the Center for Immigration Studies. Both sides have already begun running ads.

But critics also have important grass-roots influence, including from talk radio hosts who were instrumental in defeating the bill in 2007, and opponents argue that as the public absorbs the content of the legislation, the tide will turn against it. They say that there are already signs that it’s happening. Although conservative commentators on Fox News Channel and elsewhere have been more muted so far than in 2007, some talk radio hosts including Mark Levin and Rush Limbaugh have begun to voice deep unease about the bill despite the efforts of its conservative standard bearer, Sen. Marco Rubio, R-Fla., to sell the legislation to them and other conservative opinion leaders.

“The supporters promoted the bill aggressively before anybody saw the language, and certain Republicans and conservative voices sort of held their fire, but that’s beginning to change,” said Sen. Jeff Sessions, R-Ala., who was a leading voice in the Senate against the bill in 2007 and is reprising that role this time around, making floor speeches, issuing press releases and holding briefing calls with reporters to argue that the bill would unlock a much larger volume of immigration into the U.S. than advertised, to the detriment of U.S. workers and jobs.

“It’s going to be like that mackerel in the sunshine — the longer it’s out there the worse it smells,” Sessions said.

The bill would aim to boost border security, fix legal immigration and worker programs, require all employers to check their workers’ legal status and offer eventual citizenship to the estimated 11 million immigrants already living in the country illegally.

Joyce Kaufman, a host on a Florida radio station, WFTL, said that opposition to the bill was soft at first but grows daily.

“Yes, we believe this is amnesty,” Kaufman said. “Citizen activists are outraged.”

Lott said that supporters of the legislation still haven’t come up with an argument as concise and effective as that one word — “amnesty” — from opponents. He said he’s spoken with Rubio, among others, to make clear that supporters of the bill need to hone their arguments.

“Last time our explanation was three paragraphs. Theirs was a word,” Lott said. When that happens, he said, “You’re dead.”

The Democratic-led Senate, where the Judiciary Committee takes up the bill on Thursday, is already going to be a tough challenge. But if the bill does pass the Senate, opponents are betting it gets stopped in the Republican-led House. A bipartisan group of House lawmakers has been promising for months to release their own bill mirroring elements of the Senate legislation but taking a tougher tack. So far they haven’t delivered.

Meanwhile, to the dismay of immigration advocates, the chairman of the House Judiciary Committee has announced plans to move forward with individual, single-issue immigration bills, rejecting the comprehensive approach in the Senate that’s backed by President Barack Obama, who’s made immigration legislation a top second-term priority. The legislation was also a priority in 2007 for then-President George W. Bush, but he was unsuccessful in persuading Republican lawmakers to get behind the bill, and Democrats who at the time controlled Congress were divided, too.

In the 2007 debate, a turning point came when the conservative Heritage Foundation released a report saying that the legislation would cost taxpayers $2.6 trillion, including benefits to immigrants and other expenditures. Although the analysis was disputed it carried weight with GOP lawmakers. Now under the leadership of former Sen. Jim DeMint, R-S.C., another lead opponent of the legislation in 2007, Heritage was releasing an updated version of that report on Monday claiming that the new bill costs a whopping $6.3 trillion. That’s mostly from more than $9 trillion in government benefits Heritage says would go to newly legalized immigrants over their lifetimes, only partly counterbalanced by $3 trillion they would pay in taxes.

In a sign of how supporters of the bill are working hard not to repeat mistakes from the past, conservative groups that support the legislation sought in advance to pre-empt the Heritage report, with the Cato Institute deriding it ahead of time as “fatally flawed,” and Cato and others arguing that immigration reform would boost the economy by growing the labor market. Nonetheless officials with Heritage argue their report could have the same impact this time around as in 2007.

“There’s been a lot of posturing, a lot of talk. We haven’t really gotten to the heart of the debate yet,” said Dan Holler, communications director for Heritage Action for America, the Heritage Foundation’s activist arm. “We have the right policy, the numbers are going to be there, and the debate is going to shift. And no amount of ads will be able to shift it back.”