Matt. 5:17-18 is interestingly quoted because it seems to denote the idea that we should still be circumcised, not eat pork, etc. I believe this statement is refering to The Law, written by God himself on clay tablets, The Ten Commandments.
I, personally, do not support our government's use of the death penalty because, all too often, innocent people are condemned to death. But this "innocent" idea itself brings up an important question (vaguely alluded to in the article). If Jesus supports the death penalty because He is God and God demands death for sin; then who among us is left out of this punishment? No one. So I begin to think that Jesus death being carried out for my sin, once for all, has satisfied this righteous demand of God. There is only one sin left to commit, blaspheming the Holy Spirit (e.g. not accepting Christ). If capital punishment is still a necessary punishment for sinners, then Christ's death means little; and ultimate punishment still awaits the unrepentant.

There is no evidence of Jesus supporting capital punishment.
Jesus was a Pharisee. Pharisaic reforms to the law at that period included making the law more humane, especially the penal code. The “lex talionis” was interpreted to mean that compensation should be paid in money for an injury.

Capital punishment was not abolished but was hedged around with so many conditions and qualifications it was rarely ever carried out. Evidence had to be clear to an absolutely unequivocal degree. There had to be two eye-witnesses’ as circumstantial evidence or even a confession was not admissible.

Josephus wrote of the humanity of the Pharisees in penal matters and stated that they “tend to be lenient in punishments” (Antiquities xiii. 10.6). However, the Sadducees accepted the Biblical penal code in its harshest literal sense.

So the likely answer to your question is that Jesus the Pharisee would have demanded a lot of hard evidence before he and his fellow judges condemned anyone