The campaigns of U.S. Sen. Ted Cruz, R-Texas, and Democratic challenger U.S. Rep. Beto O'Rourke were said to be near a deal for debates ahead of their U.S. Senate showdown in November.

Cruz has repeatedly criticized O'Rourke for refusing his proposal of five debates – beginning Friday – ahead of the general election. O’Rourke, in turn, has accused Cruz and his campaign of dictating the terms of the proposed debates, the Houston Chronicle reported.

“One of the challenges we’ve had is that Senator Cruz not only attempted to dictate the date, the place, the time, um, also the moderators, the subjects that we could talk about,” O’Rourke told Houston Public Media.

So far the candidates' back-and-forth has come in the form of responses to the other's campaign ads and other rhetoric.

The Cruz campaign recently launched an ad accusing O'Rourke of voting against tax relief for Hurricane Harvey, which devastated southeastern Texas a year ago.

But O'Rourke said at the time that he didn't support the bill because the broader legislation lacked funding for other important programs. He added Tuesday that he supported other Harvey-related bills that directed more than $90 billion to hurricane victims, the Texas Tribune reported.

Meanwhile, the Texas Republican Party on Tuesday turned up the heat on O'Rourke, posting several old photos of the Democrat in a bid to convince him to debate Cruz.

One post shows a mugshot of O’Rourke from a 1998 DUI arrest. The accompanying text by the Texas GOP hints that perhaps the candidate was too impaired to debate Cruz.

Another photo shows a young O’Rourke with his punk rock band.

“Sorry, can’t debate. We have a gig,” the text added by the Texas GOP reads.

Yet another photo of O’Rourke includes a scrawled caption, with the candidate supposedly writing that he couldn’t debate Friday because he “just got this killer board.”

O'Rourke supporters, however, were quick to mock the Texas GOP posts.

‘“This makes me like him more,” one Twitter user wrote. “We need elected officials who’ve lived life, who aren’t walking corpses in suits. #backfire”’

“Definitely don’t want to vote for this cool guy who did fun stuff and had friends,” another user wrote.

The Texas GOP shot back, labeling would-be Beto supporters as ‘“Buzzfeed contributors, out of state liberals, and people who use the word “rad.”’

Chris Evans, O'Rourke's spokesman, said O'Rourke's brushes with the law are old news.

"Beto talks about his arrests openly and often" and "has since his first campaign ever," Evans told the Associated Press in an email.

O’Rourke, for his part, was forthcoming in op-ed for the Houston Chronicle about his past. He said he spent a night in El Paso County jail in 1995 for jumping a fence at the University of Texas at El Paso, and was arrested three years later for drunken driving. He wasn't convicted in either case, he said.

After an event in Austin on Tuesday, O'Rourke said both his and Cruz's campaigns were talking about debating, the Houston Chronicle reported.

"I'm confident we'll work something out," O'Rourke said. "I'm pretty confident we're going to see debates."

The Associated Press contributed to this report.