There are Christians who believe that the Bible makes a case for this country's obligation to protect Israel. Do Christians have this biblical command?
There may be political and economic factors involved in our stance as a nation to defend Israel, but your question concerns our biblical obligation to support Israel.
The primary text would be found in Genesis 12:1-3:
1 Now the Lord said to Abram, "Go out from your country, your relatives, and your father's household to the land that I will show you. 2 Then I will make you into a great nation, and I will bless you, and I will make your name great, in order that you might be a prime example of divine blessing. 3 I will bless those who bless you, but the one who treats you lightly I must curse, and all the families of the earth will pronounce blessings on one another using your name" (Genesis 12:1-3, NET Bible).
God chose to bless the world through Abraham. This is because the Messiah, Jesus Christ, would come to us through Abraham's seed:
16 Now the promises were spoken to Abraham and to his descendant. Scripture does not say, "and to the descendants," referring to many, but "and to your descendant," referring to one, who is Christ (Galatians 3:16, NET Bible).
The important point regarding our relationship to the nation Israel is the promise of blessing and cursing found in Genesis 12:3. In the most absolute sense, blessing and cursing comes as the result of our response to Jesus Christ.
We see this in Acts 3:25-26 (and the surrounding context):
25 You are the sons of the prophets and of the covenant that God made with your ancestors, saying to Abraham, 'And in your descendants all the nations of the earth will be blessed.' 26 God raised up his servant and sent him first to you, to bless you by turning each one of you from your iniquities" (Acts 3:25-26).
There is also a more general promise of blessing and cursing in Genesis 12:3. Those who bless the nation Israel will be blessed (not saved, but prospered in an earthly way); those who curse Israel can expect divine judgment. We see divine cursing in Zechariah 2:6-10:
6 "You there! Flee from the northland!" says the Lord, "for like the four winds of heaven I have scattered you," says the Lord. 7 "Escape, Zion, you who live among the Babylonians!" 8 For the sovereign Lord says to me that for his own glory he has sent me to the nations that plundered you-for anyone who touches you touches the pupil of his eye. 9 "I am about to punish them in such a way," he says, "that they will be looted by their own slaves." Then you will know that the sovereign Lord has sent me. 10 "Sing out and be happy, Zion my daughter! For look, I have come; I will settle in your midst," says the Lord (Zechariah 2:6-10).
When Habakkuk complains to God that the Jews are living in sin, God assures the prophet that judgment is coming upon Judah at the hands of the Babylonians (Habakkuk 1:1-11). Habakkuk then protests that the Babylonians are worse sinners than the Jews. God tells Habakkuk that while this nation will be used as His chastening rod, He will judge them for their violence against His people (Habakkuk 2). Even when one is God's chastening rod against God's people, there is still a curse, it would seem, for oppressing Israel (or, more accurately in this text, Judah).
Personally I do not believe this means that we should sanction and support every action Israel takes at this moment in time. They are in the land, but they are also in unbelief regarding Jesus, their Messiah. If they commit acts of atrocity or terrorism, they should be censored for it. But having said this we must recognize that God has committed Himself to bless Israel, and thus we should not oppose those whom God has chosen to bless; rather we should support them:
25 For I do not want you to be ignorant of this mystery, brothers and sisters, so that you may not be conceited: A partial hardening has happened to Israel until the full number of the Gentiles has come in. 26 And so all Israel will be saved, as it is written: "The Deliverer will come out of Zion; he will remove ungodliness from Jacob. 27 And this is my covenant with them, when I take away their sins." 28 In regard to the gospel they are enemies for your sake, but in regard to election they are dearly loved for the sake of the fathers. 29 For the gifts and the call of God are irrevocable (Romans 11:25-29).