When a prophet delivers a harsh warning of destruction, the proper response is repentance, not violence against the messenger. To protect Jeremiah from the death penalty, the elders of the people step forward and present a powerful historical precedent from the days of King Hezekiah.
They address those who wish to execute Jeremiah by reminding them of Hezekiah's proper reaction to a similarly severe prophecy in the past [רד״ק]. The elders ask rhetorically whether Hezekiah and his generation killed the prophet for delivering such difficult news. Even though the prophecy was deeply unpleasant to hear, they did not harm the messenger [מצודת דוד, ביאור שטיינזלץ].
Instead of lashing out, King Hezekiah humbled his proud heart and feared God [רד״ק]. The primary approach among commentators is that the king then turned to prayer, pleading before God to cancel the severe decree. In response to this sincere plea, God relented and withdrew the disaster He had planned.
Drawing a direct lesson from this history, the elders issue a grave warning about their current situation. They caution that if the people fail to act like Hezekiah, and especially if they murder Jeremiah, they will bring a massive disaster upon their own souls. Rather than moving God to cancel His decree, killing the prophet would only add a terrible crime to their existing sins and greatly increase the tragedy that will fall upon them.