"Speaking at a televised CNN event in McAllen, Texas, on Thursday, O'Rourke recounted the debate with the incumbent senator earlier this week, in which he labeled Cruz as "Lyin' Ted".
O'Rourke then said he likens impeachment to an indictment.
Rep. Beto O'Rourke, D-Texas, said Thursday he has not changed his mind about impeaching President Donald Trump - but Congress should await the finish of special prosecutor Robert Mueller's Russian Federation probe.
Ted Cruz Gets Asked About Civility, Acts Very Uncivil :: Politics :: News :: Ted Cruz :: Paste
His going negative was viewed as O'Rourke trying to make up ground with Election Day looming, but O'Rourke told Bash that borrowing from Trump's playbook was "not something that I feel totally comfortable with". "Do you believe in perjury?" the second protester joined in as Cruz was walking through the airport.
Cruz defended Kavanaugh and later voted in favor of his confirmation after allegations of sexual misconduct surfaced shortly before the confirmation vote was held, which delayed the process.
When CNN's Dana Bash asked him whether he would rule out ever running for president, O'Rourke hedged.
O'Rourke also denied Cruz's assertion that his use of the nickname was planned ahead of time, as suggested by pollsters.
The rally is set to begin at 6:30 p.m.
An ex-punk rocker giving up his congressional seat to challenge Cruz, O'Rourke has shattered fundraising records and attracted glowing national attention as he tries to become Texas' first Democrat to win statewide office since 1994.
Among registered voters, though, Cruz's lead is just 5 percentage points in the CNN poll, and O'Rourke insists that most polls don't capture the likelihood of ballots cast by many younger Texans and other newly registered voters his campaign has inspired.