Yes, the US Government did outlaw polygamy. But that wasn't the reason that the Church abandoned the Practice. The US Government outlawed it, and the Mormon Saints of the day were willing to lay down and die for their religious convictions. But they were under a lot of controversy under the subject which led the leaders of the church to go to the Lord in prayer and ask the Lord what they should do. The answer is recorded in an Official Declaration by the church. The Current Prophet at the Time (Wilford Woodruff) wrote: "The Lord showed me by vision and revelation exactly what would take place if we did not stop this practice. If we had not stopped it, you would have had no use for . . . any of the men in this temple at Logan; for all ordinances would be stopped throughout the land of Zion. Confusion would reign throughout Israel, and many men would be made prisoners. This trouble would have come upon the whole Church, and we should have been compelled to stop the practice. Now, the question is, whether it should be stopped in this manner, or in the way the Lord has manifested to us, and leave our Prophets and Apostles and fathers free men, and the temples in the hands of the people, so that the dead may be redeemed. A large number has already been delivered from the prison house in the spirit world by this people, and shall the work go on or stop? This is the question I lay before the Latter-day Saints. You have to judge for yourselves. I want you to answer it for yourselves. I shall not answer it; but I say to you that that is exactly the condition we as a people would have been in had we not taken the course we have.  
. . . I saw exactly what would come to pass if there was not something done. I have had this spirit upon me for a long time. But I want to say this: I should have let all the temples go out of our hands; I should have gone to prison myself, and let every other man go there, had not the God of heaven commanded me to do what I did do; and when the hour came that I was commanded to do that, it was all clear to me."