DALLAS (CBSDFW.COM) – Texas Senator Ted Cruz told CBS 11 Thursday, Feb. 11, he and his family have had to take precautions to protect themselves against death threats.

“I will say the nasty rhetoric on the other side, the death threats directed at me and directed at my family have increased substantially, and we’ve seen this across the board. I think everyone needs to calm down. I’m going to do my job. I’m not going to be intimidated.”

Senator Cruz has come under fire after he led the effort in the Senate to object to certifying Arizona’s and Pennsylvania’s results in the 2020 election – before and after the deadly riot at the Capitol on January 6.

Texas Democrats demand he resign.

The Republican Accountability Project has placed electronic billboards around North Texas and other areas in the state accusing him of lying about the election and calling for him to step down. “We’ve had four years of our country being torn apart, people engaged vicious, angry, and personal assaults and these billboards are a manifestation of that. I ain’t going anywhere.”

At the Senate impeachment trial Thursday, the Democratic House Impeachment Managers argued former President Donald Trump incited the violent Capitol attack because some of the accused rioters said they were doing what he wanted.

They also said Mr. Trump showed no remorse after the attack.

Attorneys for the former President have said the rioters acted on their own.

In his interview Thursday morning, Cruz said, “It’s clear on January 6th, there was a terror attack on the Capitol. It was horrific. It was violent. It was criminal. It resulted in the murder of a police officer, and every single person who participated in that violent attack, should be fully prosecuted.”

But Cruz said the former President shouldn’t be held responsible. “If words like “fight” and “win” and “take back our country” now satisfy the standard for incitement, then every political candidate in the country all the way down to dog-catcher is about to be prosecuted for incitement. Look, his rhetoric at times is over-heated, and I’ve disagreed with some of the language the President has used, but under any fair measure it doesn’t meet the legal standard for incitement.”

He has said a former President can face an impeachment trial after he or she leaves office, but said the Senate has the jurisdiction to decide whether to hold the trial.

Cruz said in this case, he voted to dismiss the case. “The House didn’t follow due process. It didn’t provide any due process at all. The entire impeachment took seven days, they held zero hearings, they heard no witnesses. This was a political judgment.”

He predicted the former President won’t be convicted. “This trial is going to end with an acquittal. It takes 67 votes to convict President Trump. There aren’t 67 votes in the Senate. So right now, Senate Democrats are going through, expressing their anger at the President, but it’s all for naught.”

WATCH FULL INTERVIEW HERE