Constitutional democracies are very young compared to the Bible’s long history. Still, biblical principles about government clearly require that we be involved in their direction. And the Apostle Paul has strong words for those who say, "He's not MY president!"
Roughly, only half of the Evangelical Christians in America are registered to vote, and of those, half make it to the polls on any given election.
This instruction was given to Jews exiled in Babylon. Though their first allegiance was to their ancestral homeland, God insisted that they become civically involved in Babylon. American Christians can’t claim their spiritual citizenship in heaven absolves us from our responsibility to pray and care about what happens to our nation and neighbors. And our primary influence in our government is our vote.
Representative government was actually the first way the Israelite government was organized under Moses. Exodus 18:21 ESV - Moreover, look for able men from all the people, men who fear God, who are trustworthy and hate a bribe, and place such men over the people as chiefs of thousands, of hundreds, of fifties, and of tens.
Ability was a necessary requirement for selecting those leaders, but so was character. It’s an indictment on voters that moral compromise and eventual corruption is expected from our politicians. Though unbelievers may not have the same expectations for their elected officials, leaders in the church are given these requirements in 1 Timothy 3:1-16 ESV - The saying is trustworthy: If anyone aspires to the office of overseer, he desires a noble task. Therefore an overseer must be above reproach, the husband of one wife, sober-minded, self-controlled, respectable, hospitable, able to teach, not a drunkard, not violent but gentle, not quarrelsome, not a lover of money. He must manage his own household well, with all dignity keeping his children submissive, for if someone does not know how to manage his own household, how will he care for God's church? It follows that Christians should use their vote to hold their elected officials accountable by the same measure.
Joseph de Maistre wrote that “every nation gets the government it deserves.” This particularly true of democracy, where, all too often, the voice that appeals to the lowest common denominator prevails. It's unfortunate that character and wisdom take a back seat to the excitement of empty promises. Proverbs 28:2 ESV - When a land transgresses, it has many rulers, but with a man of understanding and knowledge, its stability will long continue.
Have you heard professing Christians disrespect the office of the president, use only the president’s first or last name when referring to him, or say, “he’s not MY president”? After a decade of persecution and debauched rule by the Roman Empire, the Apostle Paul wrote this in Romans 13:1 - Let every person be subject to the governing authorities. For there is no authority except from God, and those that exist have been instituted by God.
The Bible holds many examples of God allowing an ungodly leader for the sake of His judgement on a nation or empire. Christians are not called to insult or rebel against authority. We are called to pray for our leaders, and to respectfully (Romans 13:7) use civil means to work toward a government and nation that mirrors biblical values.