Matthew 2:5-6

They told him, “In Bethlehem of Judea, for this is what the prophet wrote: ‘And you, Bethlehem, in the land of Judah, are no longer least among the princes of Judah; for out of you shall come a Governor, who will shepherd My people Israel.’”
Matthew 2:5-6, Modern English Version (MEV)
 
It would be difficult at this point to say with any certainty whether the Jewish leaders were troubled over this announcement of the birth of the King of the Jews, but considering the type of person Herod was, it would be easy to believe that they were more than a bit concerned. There was a general hope and expectation that the promised Messiah would come soon, and nowhere was this hope greatest than in Jerusalem, where the iron fist of Herod, and his Roman masters, was felt the greatest. The city seethed under the surface, with open rebellions breaking out periodically, only to be ruthlessly put down by Herod and the Romans. Whatever their feelings at that moment, they were well versed in the prophecies of their coming King who would conquer all of Israel's enemies and rule them with a might hand.
 
Some additional background from Adam Clarke’s Commentary on the Bible:
 
In Bethlehem of Judea: for thus it is written by the prophet - As there have been several confused notions among the Jews, relative not only to the Messiah, and his character, but also to the time of his birth, it may be necessary to add, to what has already been said on this subject, the following extracts from the Talmudists and Gemarists, quoted by Lightfoot. At the close of a long dissertation on the year of our Lord’s birth, (which he places in the 35th of the reign of Herod, not the last or 37th as above), he says: “It will not be improper here to produce the Gemarists themselves openly confessing that the Messias had been born, a good while ago before their times. For so they write: After this the children of Israel shall be converted, and shall inquire after the Lord their God, and David their king: Hos_3:5. Our rabbins say, That is King Messias, If he be among the living, his name is David, or if dead, David is his name. R. Tanchum said, Thus I prove it: He showeth mercy to David his Messiah. (Psa_18:50). R. Joshua ben Levi saith, His name is צמח tsemach, a Branch. (Zec_3:8). R. Juban bar Arbu saith, His name is Menahem. (That is, παρακλητος, the Comforter). ‘And that which happened to a certain Jew, as he was ploughing, agreeth with this business. A certain Arabian travelling, and hearing the ox bellow, said to the Jew at plough, O Jew, loose thy oxen, and loose thy ploughs, for behold! The temple is laid waste. The ox belloweth the second time; the Arabian saith to him, O Jew, Jew, yoke thy oxen, and fit thy ploughs: והא יליר מלכא משיחא For behold! King Messiah is born. But, saith the Jew, What is his name? Menahem, saith he (i.e. the Comforter). And what is the name of his Father? Hezekiah, saith the Arabian. To whom the Jew, But whence is He? The other answered, From the palace of the king of Bethlehem Judah. Away he went, and sold his oxen and his ploughs, and became a seller of infants’ swaddling clothes, going about from town to town. When he came to that city, (Bethlehem), all the women bought of him, but the mother of Menahem bought nothing. He heard the voice of the women saying, O thou mother of Menahem, thou mother of Menahem, carry thy son the things that are here sold. But she replied, May the enemies of Israel be strangled, because on the day that he was born, the temple was laid waste. To whom he said, But we hoped, that as it was laid waste at his feet, so at his feet it would be built again. She saith, I have no money. To whom he replied, But why should this be prejudicial to him? Carry him what you buy here, and if you have no money today, after some days I will come back and receive it. After some days, he returned to that city, and saith to her, How does the little infant? And she said, From the time you saw me last, spirits and tempests came, and snatched him away out of my hands. R. Bon saith, What need have we to learn from an Arabian? Is it not plainly written, And Lebanon shall fall before the powerful one? (Isa_10:34). And what follows after? A branch shall come out of the root of Jesse. (Isa_11:1).
 
“The Babylonian doctors yield us a confession not very unlike the former. R. Charinah saith: After four hundred years are passed from the destruction of the temple, if any one shall say to you, Take to thyself for one penny a field worth a thousand pence, do not take it. And again, After four thousand two hundred thirty and one years from the creation of the world, if any shall say to you, Take for a penny a field worth a thousand pence, take it not. The gloss is, For that is the time of redemption, and you shall be brought back to the holy mountain, to the inheritance of your fathers; why, therefore, should you misspend your penny?
 
“You may fetch the reason of this calculation, if you have leisure, out of the tract Sanhedrin. The tradition of the school of Elias, the world is to last six thousand years, etc. And a little after, Elias said to Rabh Judah, The world shall last not less than eighty-five jubilees: and in the last jubilee shall the Son of David come. He saith to him, Whether in the beginning of it, or in the end? He answered him, I know not. Whether is this whole time to be finished first, or not? He answered him, I know not. But Rabh Asher asserted, that he answered thus, Until then, expect him not, but from thence expect him. Hear your own countrymen, O Jew! How many centuries of years are passed by and gone from the eighty-fifth jubilee of the world, that is, the year MMMMCCL, and yet the Messias of your expectation is not yet come!
 
“Daniel’s weeks had so clearly defined the time of the true Messias, his coming, that the minds of the whole nation were raised into the expectation of him. Hence, it was doubted of the Baptist, whether he were not the Messias, Luk_3:15. Hence it was, that the Jews are gathered together from all countries unto Jerusalem, Acts 2:, expecting and coming to see, because at that time the term of revealing the Messias, that had been prefixed by Daniel, was come. Hence it was that there was so great a number of false Christs, Mat_24:5, etc., taking the occasion of their impostures hence, that now the time of that great expectation was at hand, and fulfilled: and in one word, They thought the kingdom of God should presently appear, Luk_19:11.
 
“But when those times of expectation were past, nor did such a Messias appear as they expected, (for when they saw the true Messias, they would not see him), they first broke out into various, and those wild, conjectures of the time; and at length, all those conjectures coming to nothing, all ended in this curse (the just cause of their eternal blindness) של מתשכי קצי הפת רות, May their soul be confounded who compute the times!” They were fully aware that the time foretold by the prophets must be long since fulfilled; and that their obstinacy must be confounded by their own history, and the chronology of their own Scriptures; and therefore they have pronounced an anathema on those who shall attempt to examine, by chronological computations, the prophecies that predict his coming. Who can conceive a state of willful blindness or determined obstinacy superior to this!
 
And thou Bethlehem, in the land of Juda - To distinguish it from Bethlehem, in the tribe of Zebulon. Jos_19:15. See on Mat_2:1 (note).
 
Art not the least - In Mic_5:2, it is read, Though thou be little - צעיר להיות tsdir lehayoth, little to be. Houbigant, struck with the oddness of the construction of the Hebrew, by dividing the last word, and making a small change in two of the letters, makes the prophet agree with the evangelist, צעיר לא היית ,tsilegna tsdir lo hayita, thou art not the least. Several learned men are of opinion, that the copy from which St. Matthew quoted, had the text in this way. However, some MSS. of very good note, among which is the Codex Bezae, have μη ελαχιστη ει, for ουδαμως ελαχιστη ει, Art thou not the least? This reconciles the prophet and evangelist without farther trouble. See the authorities for this reading in Griesbach and Wetstein.
 
Among the princes of Juda - In Mic_5:2, it is, the thousands of Judah. There is much reason to believe that each tribe was divided into small portions called thousands, as in England certain small divisions of counties are called hundreds. For the proof of the first, the reader is referred to Jdg_6:15, where, instead of my Family is poor in Manasseh, the Hebrew is, my Thousand (אלפי) is the meanest in Manasseh: and to 1Sa_10:19, Present yourselves before the Lord by your Tribes and by your Thousands: and to 1Ch_12:20, Captains of the Thousands of Manasseh. Now these Thousands being petty governments, Matthew renders them by the word ηγεμοσιν, because the word princes or governors was more intelligible in the Greek tongue than thousands, though, in this case, they both signify the same. See Wakefield.
 
That shall rule my people Israel - Οστις ποιμανει, Who shall Feed my people. That is as a shepherd feeds his flock. Among the Greeks, kings are called, by Homer, λαων ποιμενες, shepherds of the people. This appellation probably originated from the pastoral employment, which kings and patriarchs did not blush to exercise in the times of primitive simplicity; and it might particularly refer to the case of David, the great type of Christ, who was a keeper of his father’s sheep, before he was raised to the throne of Israel. As the government of a good king was similar to the care a good shepherd has of his flock, hence ποιμην signified both shepherd and king; and ποιμαινω, to feed and to rule among the ancient Greeks.