The laws on child marriage have been a disgrace in the US for a long time. The reason that change on a national level would be very difficult is that the Constitution of the United States, in its division of powers provisions, essentially makes marriage laws the province of the states. Changing the Constitution is a very cumbersome process.
The more likely avenue is doing it state by state, which is happening, although much more slowly than I would like. Delaware recently became to first state to institute an absolute ban, making marriage under the age of 18 illegal. My own state, Florida, has the next most stringent law, enacted earlier this year. In Florida the age for marriage is 18, with one exception: 17 year-olds can marry with parental consent, but to no one more than two years older. Just as an observation, that makes Delaware and Florida actually more protective of people under the age of 18 than any of the countries in the UK.
Other states have recently enacted laws that limit the exceptions to marriage of minors, though none are as stringent as Delaware and Florida. Activists are working to make changes in many other states.
Semantics in important here, too. When people in the US talk about child marriage, they generally mean anyone under the age of 18, which is the age of majority in all states (also a matter of state law). So by that understanding, child marriage is legal in the UK as well for 16 and 17 year olds (and without parental consent in Scotland).