Outside a Senate Republican lunch on Tuesday, Ted Cruz lashed GOP leaders for their plan on immigration, telling reporters that it’s a “strategy designed to lose.”

Inside the GOP lunch, Cruz was mum and didn’t raise the issue at all, according to three senators at the gathering.

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As he prepares for a likely presidential run, the Texas Republican senator is proceeding cautiously on the latest controversy engulfing the Senate. He is trying to showcase his role as a leading agitator, pulling a recalcitrant Republican establishment to the right. But with his party now struggling to find a way out of an immigration jam, pushing conservatives to take a hard line could result in a standoff with the White House and a politically damaging shutdown of the Department of Homeland Security — just as Cruz prepares to roll out his presidential campaign.

Unlike the battle over Obamacare that prompted the government shutdown in 2013, Cruz is keeping his distance from this latest fight, blaming GOP elders and Democrats for the mess — while taking an unusually low-profile role despite his own outspoken opposition to the president’s immigration policies last year.

Through Tuesday evening, Cruz had not delivered a single speech on the floor over the past week when the issue has dominated the Senate. (His like-minded conservative colleague, Alabama Sen. Jeff Sessions, has spoken for 147 minutes about the topic since Feb. 2.) At several lunches where the issue was discussed, Cruz was either silent on the immigration matter or spoke sparingly, senators said. And even at a private Republican retreat last month in Pennsylvania, Cruz skipped a Senate strategy session where the party’s leadership and committee chairmen laid out a game plan for the first several weeks of the new Congress and discussed the immigration fight, attendees said.

It was a sign of how Cruz has to balance his message as a conservative firebrand who says he’s not afraid to “stand and lead” while dealing with the legislative realities in Washington — and the fact that he dines daily with Republican senators when Congress is in session. He’s willing to bash his party publicly but rarely singles out GOP senators by name. And after coming under tremendous heat from his own party during the government shutdown, including being berated behind closed doors, Cruz has avoided private confrontations with GOP senators over the tactics they are pursuing.

“No,” Sen. Jeff Flake (R-Ariz.) said when asked if Cruz had raised concerns about the immigration matter in private lunch meetings.

“Not when I’ve been there,” said South Dakota Sen. John Thune, No. 3 in Senate GOP leadership, when asked if he’d heard Cruz raise private objections to the latest immigration strategy.

The back and forth over immigration highlights the larger problems facing Republicans as they deal with their first messy legislative fight since taking control of the Senate last month. In the aftermath of President Barack Obama’s post-election move to defer deportations for roughly 5 million undocumented immigrants and pave the way for them to obtain work permits, Republicans have been struggling to find a strategy to push back effectively.

Cruz, one of the most furious critics of what he refers to as Obama’s “executive amnesty,” pushed his party’s leaders to include in a mega-funding bill late last year a provision to block the actions. But GOP leaders, nervous about another government shutdown immediately after they won big in November’s elections, cut a deal with Senate Democrats, who were still in control of the chamber at the time, as well as the White House. They pushed through a compromise omnibus spending package that funded virtually the entire government through the end of September but temporarily extended money for DHS until Feb. 27.

The idea, Republicans said, was to fight the president’s immigration strategy when it was time to consider the budget for DHS, the agency that enforces immigration laws, when the party assumed control of both chambers in 2015. So last month, House Republicans included in the $39.7 billion DHS funding bill a provision to block Obama’s 2014 immigration policies and a 2012 move deferring deportations to undocumented immigrants brought to the country illegally at a young age.

But the GOP quickly ran into a problem: the Senate. Despite controlling 54 seats, Republicans faced a wall of opposition from Democratic senators who are demanding a “clean bill” stripped of any immigration riders. On three separate occasions last week, Democrats filibustered the bill, with Republicans falling seven votes shy of the 60 needed to bring the measure to the floor for a debate. (GOP Sen. Dean Heller of Nevada joined a united Democratic Caucus in blocking the bill.)

On Tuesday, Senate Majority Leader Mitch McConnell (R-Ky.) finally acknowledged the obvious: The chamber was “stuck.”

“I think it’s clearly stuck in the Senate, we can’t get on it, we can’t offer amendments to it,” McConnell told reporters. “And the next step is obviously up to the House.”

But House Republicans pointed back at the Senate, saying the chamber needed to pass its own bill.

The blame, Cruz said, lies squarely at the feet of party leaders.

“What I said this weekend was clear, which is this current ‘Crominbus’ bill was designed by leadership,” Cruz said Tuesday, referring to comments he made during two political shows on Sunday. “I objected strenuously at the time and made the point that it was a strategy designed to lose. My objections were overruled.”

Cruz added: “Leadership proceeded nonetheless down this path, and it’s now incumbent on leadership to explain what their path is to what they stated the end goal would be.”

Still, GOP leaders said they designed their strategy to placate immigration hard-liners like Cruz as well as to avoid a government shutdown. While Cruz voted against the December spending bill, Republicans say they could use the Texas senator’s help to pressure Democrats now.

Michael Steel, a spokesman for House Speaker John Boehner (R-Ohio), said the leadership plan was developed after extensive consultations with House Republicans.

“And while it may not be perfect,” Steel said, “it is certainly preferable to the alternative.”

Pushing on the issue in the lame-duck session, said Flake, would have been more challenging given that Republicans were still in the minority last year.

“Anything that’s tough now would have been tougher before we had a majority,” he said.

It’s not unusual for Cruz to differ with his caucus over tactics. Since joining the Senate after winning the seat vacated by then-Sen. Kay Bailey Hutchison (R-Texas) in the 2012 elections, Cruz in 2013 blocked efforts by the House and Senate to negotiate a budget resolution, arguing it would be a back-door way to raise the debt ceiling. In September 2013, he pushed House Republicans to include in a government funding bill provisions that would have defunded Obamacare, even taking to the floor for a marathon 21-hour speech. A week later, the standoff prompted a government shutdown and ample GOP recriminations over his strategy.

In February 2014, Cruz filibustered a bill to raise the debt ceiling, prompting McConnell and his fellow Texas Sen. John Cornyn, along with other Republicans, to advance the measure because they feared its failure would prompt a government default on its obligations. And in December, Cruz — along with his ally, Utah Sen. Mike Lee — effectively forced the Senate to return to Washington for a rare Saturday session in order to lodge a protest over Obama’s immigration policies. The tactic, GOP senators publicly complained, strengthened the Democrats’ hands. Cruz later apologized to his colleagues for abruptly interrupting their weekend plans, though he showed little remorse for mounting the immigration fight.

Such fights are expected to be central to Cruz’s likely presidential campaign, giving him an argument to advance that he’s battled with his party leadership over the direction of the GOP.

With the House DHS bill stalled in the Senate, Boehner has publicly called on Cruz — and Sessions — to lead the charge in their chamber.

“It’s time for Sen. Cruz and Sen. Sessions and Senate Republicans and Senate Democrats to stand with the American people and to block the president’s actions,” Boehner said last week.

But Cruz told reporters Tuesday that Boehner and McConnell had “given away virtually all our leverage by funding almost the entirety of the federal government” in last December’s funding package. Cruz also called on McConnell to prevent the confirmation of all presidential nominations who are not vital to national security interests — until Obama relents on immigration. (McConnell has ignored his call.)

Asked whether he agreed with Cruz’s criticism of the strategy so far, Sessions was cautious.

“I don’t know about that,” the Alabama conservative said. “We should fund Homeland Security, which this bill does, but we shouldn’t fund the unlawful actions the president took on immigration.”