Washington (CNN) Republican Party leaders and prominent senators are sharpening their knives against Ted Cruz, expressing growing alarm over his candidacy as he continues to mount a serious threat in Iowa.

In interviews with CNN, a growing number of Republicans are beginning to echo remarks made by the likes of former Sen. Bob Dole and Iowa Gov. Terry Branstad, warning that the party would suffer deep losses down the ticket and risk electing a Democratic president if the Texas senator wins the nomination.

"I think we'll lose if he's our nominee," said Orrin Hatch, the most senior Republican in the Senate.

"There's a lot of people who don't feel he can appeal to people across the board," Hatch said. "For us to win, we have to appeal to the moderates and independents. We can't just act like that only one point of view is the only way to go. That's where Ted is going to have some trouble."

It's not just Jeb Bush supporters like Hatch who are speaking out more aggressively. A large number of GOP senators say Cruz's divisive tactics, which have included describing his colleagues as part of a corrupt "Washington cartel," will make it hard --- if not impossible --- to get behind him if he's the nominee.

"It would be a major challenge because of the wounds that are deep," said Indiana Sen. Dan Coats, who is neutral in the race so far.

"An awful lot of us really didn't like to be targeted as corrupt, establishment bought by the lobby establishment," Coats added. "It sure looks like someone was using it as a way to gain notoriety as the only true conservative in Washington."

The bitter feelings come at an urgent time for Republicans. Cruz is neck-and-neck with Donald Trump in Iowa, and a win in the Hawkeye State could put the Texas freshman on solid ground heading into the rest of the primary contests in February. A loss in Iowa, however, could set Cruz back substantially as the race turns to New Hampshire, where Trump is running ahead of the pack and others like Marco Rubio, Jeb Bush and John Kasich are vying for second place.

There's no love for Cruz, who many in the party believe has chosen to engage in tactics aimed at dividing the GOP. He famously led the charge to defund Obamacare in 2013, a battle that precipitated a 16-day government shutdown . He battled with his party's strategy on immigration, the debt ceiling and the budget, even one time pulling GOP senators into session on a Saturday during Christmas season.

And Cruz's accusation earlier this year that Senate Majority Leader Mitch McConnell is a liar over his deal-making on the Export-Import Bank angered many Republicans.

"Ted Cruz has burned some bridges with some fellow senators," said Sen. Shelley Moore Capito of West Virginia. "You do see people coming out with more aggressive comments" ahead of Iowa.

Cruz campaign brushes off fears

Cruz's campaign is pushing back against the growing criticism from the party leaders, saying it's a concerted effort to back Trump.

"Of course D.C. establishment politicians are abandoning Marco Rubio and running to Trump, because they want a candidate who will cut deals to keep them in power, said Cruz spokeswoman Catherine Frazier.

"And that's perfectly fine, because Americans aren't looking for a dealmaker who will compromise; they are looking for a leader who will break up the Washington cartel and restore our nation's safety and prosperity," Frazier added.

Indeed, some in the party establishment do believe that Trump would have cross-over appeal, despite his incendiary comments.

"I've come around a little bit on Trump," Hatch said Thursday. "I'm not so sure we'd lose if he's our nominee because he's appealing to people who a lot of the Republican candidates have not appealed to in the past."

Worries about down-ballot impact

Sen. John Cornyn, Cruz's fellow Texas Republican and the No. 2 in his conference, said GOP senators are unsettled by the roiling presidential race and what it could mean for their chances of keeping control of the Senate, where the party has a narrow 54-46 majority and faces several tough re-election races in left-leaning states like Illinois.

"I think people are concerned," Cornyn told CNN. "Because obviously the top of the ticket will have a big bearing on whether we'll hold a majority of the Senate. We don't need any headwinds from the top of the ticket. We need some tailwinds."

Asked if he agreed with Dole's comments to The New York Times that nominating Cruz would be "cataclysmic" to the party, Cornyn said: "I'm not going to comment on that."

Others were even more forceful.

"His ability to grow the vote of the Republican Party is almost zero," South Carolina Sen. Lindsey Graham, who dropped out of the presidential race and is now backing Bush, said of Cruz. "He'll easily be portrayed as ideological to a fault."

Asked if he'd prefer Trump over Cruz, Graham said: "It's a lot like being shot or poisoned: I think you get the same result."

McCain: Cruz is no Reagan

While running against an unpopular GOP leadership undoubtedly plays well with the base, having support from the party establishment can help in the general election, with surrogates barnstorming the country and speaking on the airwaves on behalf of the nominee's agenda. It's uncertain whether that would happen with Cruz at the top of the ticket.

"There's no doubt he has harmed relationships among people," said Sen. John McCain, R-Arizona, the 2008 GOP presidential nominee. "I would assume that all members would work with the elected president for the good of the country. But there is no doubt there would be strains in the working relationship."

McCain added: "He talks a lot about Ronald Reagan. One of things that Ronald Reagan did when he came to office was heavily court Republicans and Democrats. ... I don't see Sen. Cruz being able to do that."

And the senators, it's clear, are not going to hold back.

Graham, for instance, said that Trump was "crazy" with an "insane" foreign policy and Cruz was a "rigid ideologue," both of which would be problematic against Hillary Clinton, even if voters view her as a "dishonest" candidate, he said.

"Dishonest beats crazy," said Graham, who dropped his bid for the GOP nomination last month. "Dishonest loses to normal. Just pick somebody normal. Pick somebody out of the phone book and we win."