Sen. Lindsey Graham, R-S.C., speaks to supporters after being reelected. (Rainier Ehrhardt/AP)

Sen. Lindsey O. Graham (R-S.C.) winced as he listened to comments from Rep. Michele Bachmann (R-Minn.) in reaction to President Obama’s plans to protect undocumented immigrants from deportation.

“Unfortunate, unfair, unnecessary, unwise,” Graham said.

Earlier Wednesday, Bachmann, a retiring tea-party firebrand, had declared that those immigrants covered by the policies that the president would announce Thursday would become “illiterate” voters.

For Republicans the roiling debate over the president’s decision is not only a fight with the White House, but a test of whether they can contain some of the unhelpful passions among their swelling majorities in both chambers. The task is keeping on-message and away from the controversial and sometimes offensive comments that have traditionally hindered attempts to bolster support for the party among Hispanics.

Coupled with the desire to avoid the heated rhetoric is an effort to avert another showdown over government funding, weeks after the GOP made gains in the midterm elections and a year after a 16-day shutdown significantly damaged the party’s brand.

Ahead of the president’s prime-time address Thursday, House Speaker John A. Boehner (R-Ohio) and Sen. Mitch McConnell (R-Ky.), who will be the majority leader in the next Congress, were grappling with these swirling issues, urging calm in their ranks and considering several moves they believe would be forceful responses to the president, while also keeping the government funded.

Filing a lawsuit over the president’s executive authority, pursuing standalone legislation on immigration policy and removing funding for immigration agencies are some of the ideas that have been floated by aides to Republican leaders.

“We are considering a variety of options,” McConnell said Thursday in a floor speech. He suggested that his preference would be for Republicans to avoid becoming mired in a fiscal clash during the lame-duck session, shortly before the GOP takes control of the Senate.

Many conservative lawmakers, however, are shrugging off those pleas from leadership. Furious with the president, they are planning a series of immediate and hard-line actions that could have sweeping consequences. Sen. Ted Cruz (R-Tex.) said Wednesday that Obama’s executive action should be met with a refusal to vote on any more of his nominees, and on Thursday compared the action to the ancient Catiline conspiracy, a plot to overthrow the Roman Republic.

Sen. Jeff Sessions (R-Ala.), likely to be the next chairman of the budget committee, has advocated for a series of stopgap spending bills, with the intent of pressuring the president to relent. And Rep. Steve King (R-Iowa) has hinted at possibly bringing up impeachment measures.

But amid the chatter over strategy, it is the tone of outraged rank-and-file members that most worries GOP elders. Ahead of the 2016 presidential election, they do not want to see Republicans tagged by Democrats as hostile toward Hispanics. Even as they battle the president on legal and legislative grounds, they would like to see Republicans shore up support with immigrants and their families.

“We’ve had numerous discussions about that it is necessary,” said Sen. John McCain (R-Ariz.). “It only takes a couple” of comments for an unflattering narrative to build about the Republican response. “That’s the trouble with having some of these new young punks around here. They ought to listen to us old geezers.”

In the House, Rep. Mario Diaz-Balart (R-Fla.), who has been a prominent backer of comprehensive immigration reform, has been counseling House Republicans about the need to show empathy for undocumented workers as the party rails against the Obama administration, according to GOP aides familiar with his deliberations.

Rep. Charlie Dent (R-Pa.), a moderate from the Philadelphia exurbs and a Boehner ally, said the leadership is asking his colleagues to “not play into the president’s hands.”

“The president wants to see an angry and intemperate response, thinking the Republicans will do something that leads to a shutdown,” Dent said. “Don’t take the bait and don’t have a hysterical reaction. We can be strong, rational and measured.”

Yet the firestorms have continued to flare, with some Republicans, encouraged by grass-roots activists and conservative media personalities, eschewing the party’s more incremental line and making contentious statements.

Speaking with reporters, Bachmann had said the “social cost” of Obama’s immigration policies would be extensive, with “millions of unskilled, illiterate, foreign nationals coming into the United States who can’t speak the English language.”

When pressed on why she used the term “illiterate,” Bachmann said, “I’m not using a pejorative term against people who are non-American citizens. I’m only repeating what I heard from Hispanic Americans down at the border.”

In a Thursday interview with CNN, King said, “We have constitutional authority to do a string of things. [Impeachment] would be the very last option, but I would not rule it out.”