This is one of those weird right-wing talking points that can be easily disproved. I think this disingenuous discourse contributes to Fox News viewers' perception that crime in the US is out of control when it's actually at its lowest in decades in most cities.
The US does have capital punishment as a federal penalty, but it is not commonly used. There are particular "aggravating" factors to a federal murder charge that can make it eligible for the death penalty.
Capital sentences are far more likely punishments at the state level, and a little more than half of the states still use the death penalty.
Those Republicans aren't gone. They're just Democrats now because the entire spectrum of political discourse in the US has shifted that far right.
Remember when the Cheneys found themselves on the outs with the Republicans? Their alliance with Dems would have been utterly unthinkable 25 years ago, but look at them now. As Republicans move further right and Democrats keep trying to court "centrist" voters, all they're doing is moving their party to the right.