Sen. John McCain, R-Ariz., warned Republican campaign operatives not to use Democrats’ support for an immigration overhaul against them in 2014, saying the party should “look back” at previous electoral failures with Hispanic voters and “re-evaluate what they are saying.”

The Senate on Thursday approved major immigration law changes that were authored in part by McCain.

In a story reported by The Hill earlier Thursday, a National Republican Senatorial Committee spokesman said vulnerable, red state Democrats who voted “yes” on immigration would be imperiling their re-election chances. The Capitol Hill newspaper quoted NRSC spokesman Brad Dayspring as saying that those in-cycle Democrats are “more loyal to Chuck Schumer and Barack Obama than they are to middle-class men and women struggling in their home states.”

Fourteen Republicans voted to approve a bipartisan immigration reform framework negotiated by eight senators, including one Republican up for re-election, Lindsey Graham of South Carolina.

“Well, all I can say is maybe they ought to look back at what happened in 2012 and 2008 with the Hispanic voter, and then maybe they ought to re-evaluate what they are saying,” McCain told reporters after the vote when he was informed of the NRSC statement. “There are plenty of issues that separate Republicans and Democrats, but I don’t think [this is one, given] that a majority of Americans — 70 or 80 percent, depending on which polls you judge by — are in favor of what we are trying to do.”

Though The Hill’s report said the NRSC did not plan a “major focus” on immigration in its campaign strategy, the on-the-record statement painting supporters of the bill as beholden to the president and Schumer — a former Democratic Senatorial Campaign Committee chairman — could put Republican supporters of the bill, like Graham, in the awkward spot of falling into that same category.

Last month, the NRSC posted a video ad to attract donors called “Yes,” highlighting supporters of the immigration bill and touting the parties willingness to pass legislation.

If the NRSC does decide to use the Democrats’ immigration votes against them, it wouldn’t be the first time a party committee seemed to be at odds with itself. In 2008, Schumer used anger over the Wall Street bailout against Republicans who voted for it, including Minority Leader Mitch McConnell, R-Ky. And many Democrats who ran against incumbents that year — including current Sen. Al Franken, Minn. — also criticized their Republican opponent for voting to rescue the financial industry.

UPDATE, 6:40 p.m.: Dayspring e-mails to offer the following statement: “The NRSC hasn’t engaged on the issue or a national effort about the legislation and has no plans to. This isn’t a policy discussion, rather it is about the politics for three vulnerable Democratic Senators whom, according to public polling, face an uphill climb.  Voters in each state will decide whether their Senator’s votes represented their views.”

McCain’s warnings, even if the NRSC does not target specifically on immigration votes, are not without meaning to other outside groups who could weigh in at any time. We’ve reported previously and repeatedly the concerns held by top Republicans about losing control of their message to these groups, so even if the NRSC chooses not to engage, others could do so.