Allowing the population to force a plebiscite on an issue by gathering enough signatures is a very powerful tool that the American population have. However there are many concerns. The primary one being that is is rule by the majority, which can lead to tyranny of the majority in which minorities have no voice in politics. The founding fathers were very worried of Tyranny of the majority and as such it is a big issue with the use of initiatives. The close nature of the referendums triggered by initiatives/propositions exacerbates this problem. The majorities are often small. An example is Californian proposition 34 to abolish the death penalty. Those in favour received 48.5% of the vote, however the 51.5% against the proposition won. This example demonstrates how large portions of the population can be marginalised by initiatives/propositions.
Yet, it is the most direct form of democracy. By enabling voters to bypass their State legislatures, initiatives/propositions give the electorate a direct role in politics, enforcing popular sovereignty. Moreover, by giving the US population the power of recall, the US representatives are more accountable to their voters. Thus, further strengthening popular sovereignty. An example of a successful recall is the 2013 recall of Deedy Slaughter, Mayor of Port Allen, Louisiana. By not allowing the electorate to recall senators and representatives in congress, the system also stays relatively stable.
However, whilst the system enforces popular sovereignty, it damages the sovereignty of the legislature. By controlling or even by passing the elect officials, legislative sovereignty is infringed. Moreover, the need for many officials is diminished if the public can simply overide them.
Overall, the powers of initiatives/propositions is very strong and they are an intelligent check on States. However, they also have the potential to be abused and so need to be refined.