But on Monday, Mr. Limbaugh shed light on his interactions with the senators when he told a caller frustrated with his criticism of Mr. Rubio that the immigration position the senator had advocated “comes right out of the Gang of Eight bill.”

Mr. Limbaugh added, “I’ve had it explained to me by no less than Senator Schumer.”

Mr. Schumer declined to comment for this article. But before Mr. Obama’s re-election and soon afterward, he could hardly stop talking with conservative senators and media power brokers about the chance to pass comprehensive immigration legislation.

As early as March 9, 2011, Mr. Schumer joined Senator Lindsey Graham, Republican of South Carolina and another eventual member of the Gang of Eight, at the Palm restaurant in Manhattan, where they made their case to Mr. Murdoch, Mr. Ailes and Mr. Limbaugh in a private room. The senators argued how damaging the word “amnesty” was to their efforts, and walked Mr. Limbaugh through their vision for an immigration overhaul.

The senators were especially eager to try to neutralize conservative media, which proved lethal to a big push for immigration changes in 2007. A study by the Pew Research Center’s Project for Excellence in Journalism showed that conservative news shows had devoted about a quarter of their time to immigration.

In late 2012, after Mitt Romney, the Republican nominee, lost the presidential election in part because of his dismal performance with Latino voters, Mr. Rubio joined the fight. On one Sunday alone in April 2013, he made an appearance on seven talk shows to advocate the immigration overhaul, including on “Fox News Sunday.”

Mr. Rubio also reached out to other conservative power brokers, including the radio hosts Mark Levin and Laura Ingraham, telling them that the legislation did not amount to amnesty. The Fox anchors Sean Hannity and Bill O’Reilly became more supportive.

At the time, The Washington Post reported that Mr. Rubio’s advisers were monitoring to the minute how much time the hosts devoted to immigration, and that “they are heartened that the volume is much diminished.”