The robocalls were reported
on Thursday by The Washington Post, which talked with voters about the calls that sounded at first like surveys and then grew sharply negative about Rubio, a Florida senator, and billionaire businessman Trump.
The Post connected the calls to a firm started by Cruz campaign manager Jeff Roe, and both the Rubio and Trump campaigns were quick to point the finger at their rival as the three slug it out in South Carolina.
"We are getting reports from many voters that the Cruz people are back to doing very sleazy and dishonest 'pushpolls' on me. We are watching!" Trump tweeted
But Cruz's campaign and the firm in question denied the connection, saying they were not behind the calls.
"This is not us," Cruz spokeswoman Catherine Frazier said when asked about the accusations.
"The push polls are not coming from Cruz. Period," Cruz's rapid response director Brian Phillips tweeted in response to Trump.
And the firm, Remington Research Group, said it wasn't them, either.
"We aren't doing any robo polls in South Carolina, period. Anyone suggesting otherwise is outright lying," said Titus Bond, Remington's director.
Rubio's campaign blasted a copy of the story out to reporters, highlighting the deputy campaign manager's response.
"These tactics are becoming all too common in this race and indicative of our opponents' campaigns that are willing to say or do anything to win an election," Rich Beeson told the Post. "This is nothing more than a deliberate effort to peddle false information in the hopes of deceiving voters."
While the Rubio camp wouldn't go so far as to point the finger at Cruz themselves, they used the Post article to do it for them.
"BREAKING: @washingtonpost reports firm connected to Cruz camp is conducting push polling against Marco in SC," Rubio spokesman Alex Conant tweeted
South Carolina's primary is a week from Saturday.