These charts are from a recently released Gallup Poll. The results are an aggregate from 17 surveys they did during the year of 2016. They questioned 17,055 adults, and the results have a margin of error of only 1 point.
It shows that neither conservatism nor liberalism has the majority of the American population. Conservatism does have a bigger minority (36%) than liberalism (25%) -- but while conservatism has been slightly declining, liberalism is growing. In 2009, conservatism had a 19 point advantage. That has now been reduced to 11 points.
The reason that liberalism is growing is illustrated in the two charts below. More Democrats are now self-identifying as liberals, while less are identifying as moderates or conservatives -- and that is true of every demographic group in the Democratic Party.