That distinction is where Mr. Rubio’s campaign saw an opening and pounced. “Ted, you support legalizing people who are in this country illegally,” Mr. Rubio chided his opponent during Tuesday night’s Republican debate in Las Vegas.

But senators who were involved in the immigration fight said Mr. Cruz’s intentions were clear: He did not want to create an avenue to legalization so much as he wanted to sink the bill by striking out the path to citizenship. That would have been a nonstarter for the bill’s authors.

“This was an attempt to kill the bill,” said Senator Chuck Schumer, Democrat of New York and one of the bill’s authors. “And there was no doubt at the time that Senator Cruz knew it would do exactly that.”

Mr. Cruz’s own inconsistencies have allowed the Rubio campaign to exploit the issue. In an interview at the time the amendment was proposed, Mr. Cruz said he did not intend to stop immigration reform but to amend the bill “so that it actually solves the problem rather than making the problem worse.”

Any suggestion that Mr. Cruz is insincere in his opposition to illegal immigration could be toxic with conservative voters in the nominating contest, and Mr. Rubio’s aides realize the potential damage this could inflict. They want to whittle away at Mr. Cruz’s support among the conservative base so he does not win the Iowa caucuses, a victory that would give his campaign a bounce that could sustain him well into a pivotal round of March primaries and possibly beyond.

Mr. Cruz was at the top of the Republican field among people nationwide who identify as “very conservative,” with 33 percent support, in a statistical tie with Donald Trump (31 percent), according to the latest New York Times/CBS News poll. Ben Carson was next with 11 percent, and 8 percent of very conservative respondents said they would vote for Mr. Rubio.

How Mr. Rubio has positioned himself in the race is a fragile balancing act that Mr. Cruz and his conservative supporters are now intent on disrupting. Mr. Cruz has a luxury that Mr. Rubio does not: He is essentially running with an eye toward solidifying the conservative base. Mr. Rubio, by contrast, is trying to pull votes from factions within the Republican Party, both establishment and anti-establishment, moderate and very conservative.