Actually there are Children's Day celebrations in the US...and has been since the 1860s. It tends to be tied in with churches more so than any government recognized holiday.
Here's what's in Wikipedia:
Children’s Day observations in the United States predate both Mother’s and Father’s Day.
The celebration of a special Children’s Day in America dates from the 1860s and earlier.
In 1856, Rev. Charles H. Leonard, D.D., then pastor of the First Universalist Church of Chelsea, Mass., set apart a Sunday for the dedication of children to the Christian life, and for the re-dedication of parents and guardians to bringing-up their children in Christian nurture. This service was first observed the second Sunday in June
The Universalist Convention at Baltimore in September, 1867, passed a resolution commending churches to set apart one Sunday in each year as Children’s Day.
The Methodist Episcopal Church at the Methodist Conference of 1868 recommended that second Sunday in June be annually observed as Children’s Day.
The General Assembly of the Presbyterian Church in 1883 designated the “the second Sabbath in June as Children’s Day.”
Also in 1883, the National Council of Congregational Churches and nearly all the state bodies of that denomination in the United States passed resolutions commending the observance of the day. About this time many other denominations adopted similar recommendations.
Chase’s Calendar of Events cites Children’s Sunday and notes that The Commonwealth of Massachusetts issues an annual proclamation for the second Sunday in June.
Numerous churches and denominations currently observe the second Sunday in June including the African Methodist Episcopal Church and the Church of the Nazarene
Children's Day, was proclaimed by President Bill Clinton in October 2000. He declared that it be held on November 16th.
"National Child's Day" was proclaimed by the President of the United States of America, George W. Bush, as June 3, 2001 and in subsequent years on dates in early June. In 2003, he proclaimed June 1. In 2004, he proclaimed June 6th. In 2005, he proclaimed June 5th. In 2006, he proclaimed June 4th. In 2007, he proclaimed June 3rd. The White House Proclamation by the President of the United States of America, 2001
Nowhere in any of the proclamations did the President refer to the United Nations or the UN Resolution about Universal Child Day. It is important to note that The United States of America is one of only two countries in the world that have not ratified the United Nations Convention on the Rights of the Child. As of November 2007, 193 countries have ratified the United Nations Convention on the Rights of the Child, (UNCRC). The only other country that has not ratified the UNCRC is Somalia. United States position on the UNCRC
In 2007, Illinois Governor Rod R. Blagojevich issued a proclamation proclaiming the second Sunday in June as Children's Day. The mayors of Aurora and Batavia, Illinois, also issued proclamations.