There are ways that Christians will behave, fruit that Christ will produce in us as he lives his life in us and behaviors that are completely opposed to the new covenant. These are explained in the New Testament and many of course are based upon the foundation of the old covenant. But not all. The New Testament defines those issues for us. So, we are all under the death penalty.
Capital punishment applies to all humans.
Only Jesus Christ can save us from this sentence. The Christian response has always been governed by Romans 13. This passage teaches Christians to submit to government. This is why Christians pay taxes, are good citizens of their countries, etc. So capital punishment in the Unites States is a matter for our government and of course we are a democracy, and we can express our opinion at the ballot box.