(CNN) A quiet Republican campaign to oust Sen. Ted Cruz in next cycle's Texas primary is unfolding as the conservative firebrand has launched an aggressive effort to keep his seat ahead of another likely run for the White House.

In the wake of Cruz's controversial speech at the party convention where he refused to endorse Donald Trump, the Texas senator's GOP critics believe there could be a new opening for an intraparty challenge. And behind the scenes, GOP donors and Texas politicians have urged Rep. Mike McCaul to consider mounting a bid against him in 2018, according to three sources familiar with the matter.

McCaul, a six-term congressman who chairs the House Homeland Security Committee, has not yet deliberated on the matter but has yet to rule out a potential Senate run, according to one source close to his House reelection campaign.

George Seay, a top Texas fundraiser, said he was aware of the chatter about a challenger to Cruz and praised McCaul's talent and ability to run a competitive race, even though he counts Cruz as a longtime friend.

"Mike is very well-networked within the donor class," Seay said. "He knows an awful lot of people."

A McCaul spokesman declined to say Monday whether his boss would consider challenging Cruz, saying instead the congressman is focused on this November's elections and his committee chairmanship.

"He is also very focused on preserving the Republican majorities in Congress and winning the White House," said Walter Zaykowski, a spokesman for McCaul's House reelection campaign.

Defeating Cruz would be a tall order in the expensive state, given his deep donor network, national infrastructure and the reservoir of support he has from within the conservative movement.

Yet the 2018 race is certainly shaping up to be a distraction for the ambitious Cruz, whose aides make no bones about the 45-year-old's desire to run again in four years. Even if liberals will be hard-pressed to oust Cruz in a state that hasn't elected a Democrat statewide in decades -- let alone in a non-presidential year -- a Republican primary challenge could very well roughen up the senator and force him to use his political capital, time and money much differently.

Cruz's team is actively preparing for what they expect to be a $20 million campaign, according to a senior adviser, including in a primary challenge. Aides in recent weeks have begun reorganizing the Cruz apparatus, with some returning to his official Senate office -- such as Cruz campaign strategist David Polyansky, who began as chief of staff on Monday -- and others joining the reelection effort.

Other Cruz operatives are building new political groups that the senator will launch later this year to build his political arsenal. The political nonprofit -- to be named the Conservative Action Network -- will have a series of state-based chapters around the country.

And Cruz, who traveled around the country during his presidential campaign and spent little time in Texas, has increasingly focused his attention on his home state, including calling for a meeting this month with leaders of Texas' agriculture community that could be influential in a primary.

Cruz's advisers say they are expecting a primary challenger, in part because of the negative reaction to his speech at the Republican National Convention, where the senator was booed and shouted down by Trump supporters when he declined to offer support for the nominee. There has been little polling in Texas in so far to measure the breadth of Cruz's popularity in the aftermath of the speech.

Republicans close to Cruz hope that he will be validated by history, and that should Trump be thumped in November -- as the recent spate of polls suggests he will -- Cruz would be positioned as a soothsayer untainted by acceding to Trump's demands.

But a CNN-ORC poll shortly after last month's convention found that just 33% of GOP voters nationally had a favorable impression of Cruz, down from 60% before the convention.

Indeed, Cruz does not expect significant sour grapes from the primary once emotions thaw. Moreover, given Cruz's high-profile spats with much of his party, including over the 2013 government shutdown, Republicans say there is ample appetite to find a viable primary challenger against him.

The core senior team -- headlined by campaign manager Jeff Roe and chief strategist Jason Johnson -- is expected to remain in place for the reelection bid.

And a formal reelection launch is not expected to happen imminently after this fall's elections, but rather deep into 2017.

"You either run scared or unopposed. We always run scared," Roe told reporters about the 2018 campaign, moments after his boss was heckled by Trump supporters at a Texas delegation breakfast last month in Cleveland.

Well-placed Texans predict that the strongest primary challenge to Cruz would come from a business-allied Republican who can capture both the party's moderate wing and also the aggrieved Trump voters who felt snubbed by Cruz's high-profile non-endorsement. And sources trying to recruit McCaul into the race believe he can be convinced to run if big donors in the state decide not to put their money behind Cruz.

Cruz backlash

After the senator's speech last month, Doug Deason, who sat on Cruz's national finance committee, said he immediately fired off an email to Cruz and his wife Heidi, deeming the address "absurd" and "idiotic," he said. The next day, in Deason's retelling, Heidi Cruz replied telling him that the two "needed to talk," especially since Trump threatened to fund a super PAC against Cruz.

Deason wanted to help break peace between Cruz and Trump that weekend, hoping to arrange a meeting with Heidi Cruz and Donald Trump Jr., who both happened to be in Houston for fundraising.

Deason, now raising cash for Trump, was flying around the younger Trump on a Texas fundraising tour, and he was texting the senator's wife and other Cruz aides, desperate to set up a meeting between the camps. They were both scheduled to be in Houston that Monday.

But schedules didn't link up, according to both sides, and the meeting fell through -- even though, at one point, Trump's fundraiser was set to take place in the same Houston Italian restaurant where the Cruzes just so happened to have a dinner reservation (The Cruzes reportedly canceled.)

Primary possibilities

Much of Cruz's strength in 2018 will be determined by something beyond his control: How Trump does this November. Yet Republicans close to the campaign nevertheless predict a primary challenge, and a strong one at that.

"Prior to his running for president, no one would've thought he would've been vulnerable at all," said one senior Republican, granted anonymity to candidly assess the race.

The toughest challenger, according to conversations with a half-dozen Texas Republicans, including those linked to Cruz, is McCaul, the Houston-area congressman who is now the second wealthiest member of Congress.

The Senate GOP leadership, which has battled bitterly with Cruz, has not yet tried to court McCaul, sources said.

Republicans say McCaul is not actively making moves to launch a challenge, given that the race is still two years away. But he is hearing pitches from donors and elected officials about a possible run, and listening intently, sources said.

McCaul, who has at times clashed with Cruz, including when he considered running for the Senate in 2012, would have to sacrifice an ability to ascend up the House hierarchy for a risky Senate run. That makes some Republicans predict that he would only do so should Cruz's support erode from 2016.

Other potential names against Cruz in 2018 include Dan Patrick, the state's lieutenant governor who has become the most vocal Trump backer in the state; and George P. Bush, the up-and-coming agriculture commissioner and the scion of the presidential family.

Patrick is disappointed in Cruz, according to a person familiar with Patrick's thinking, after he was unable in the final moments to convince Cruz to endorse Trump at the RNC.

Yet both are allies of Cruz -- Patrick chaired Cruz's campaign in the state, and Bush is a personal friend of Cruz who rose through Texas politics alongside him -- and neither have the relationship with donors or the independent wealth of McCaul.

And on Monday a Patrick strategist, Allen Blakemore, said the lieutenant governor "absolutely, positively, unequivocally" won't be a candidate for Senate in 2018.

Another name buzzed about in Texas political circles: Former Gov. Rick Perry, who has become a prominent Trump surrogate in his own right. Jeff Miller, a Perry aide, said the governor was not gauging interest in a 2018 challenge.

Two Democrats have kept the door to a Cruz challenge firmly ajar in recent weeks -- giving the Texas senator an issue to use in raising money. Joaquin Castro, the Texas congressman and twin brother of the Obama cabinet official, spent the Democratic National Convention fanning the flames of a possible Cruz challenge, at one point charging that Cruz was "freaking out" over a 2018 race against him.

The other Democrat very consciously weighing her options: Wendy Davis, the state's much-buzzed about candidate for governor in 2014. Yet despite her ties to top Democrats and appeal to women and liberal activists, Davis floundered in her last statewide race for governor last cycle, disappointing Democratic leaders and setting back ambitions to turn the state blue.

Donors though have pressured Davis during recent meetings in Washington and elsewhere to consider a challenge against Cruz, according to a source close to her, and she has said publicly she is entertaining the option.

Donors push back on Cruz

Cruz has also suffered a backlash from some of his most prolific contributors, raising questions about whether he can count on his 2016 coalition to turn out again in 2018. Many major Cruz bundlers and contributors are likely to sit out of Trump's race, according to one top Cruz fundraiser, but the pockets of Trump supporters have revolted in a way that some Cruz hands did not expect.

The billionaire Sheldon Adelson refused to meet with Cruz in his suite in Cleveland immediately following the senator's RNC speech. The publicity-shy Bob Mercer, who has given over $2 million to pro-Trump efforts, took the extraordinary step of castigating Cruz in a statement to The New York Times. And a new generation of Cruz moneymen now say they are spurned, with some vowing not to raise cash for Cruz again or predicting that his fundraising will slow significantly in 2018 and more importantly, in 2020.

"I'm going to support the nominee," said Brint Ryan, a Cruz fundraiser from Texas when asked about his plans for the fall. "I'm not going to pull a Ted Cruz."

Some were more kind.

"I wish Ted had endorsed him," said Andy Puzder, a Trump fundraiser and fast food magnate who Cruz has slowly courted behind the scenes. "Politically a bad move, but Ted acts consistent with his moral code."

Cruz may be able to count on anti-Trump donors -- of which they are many -- to flock to him should Trump lose resoundingly. Mark Holden, the chief political aide to Charles and David Koch, who have pointedly not endorsed the Republican nominee, however said that the Koch network had little reaction to Cruz's speech.