The current situation, with the electoral college selecting the President, and the popular vote selecting the members of the electoral college on a variety of different schemes, varying by state, but mostly under the "winer take all" scheme where the majority winner of the popular vote in the state wins all the electoral votes of the state. The website gives a succinct explanation:
The National Popular Vote bill would guarantee a majority of the Electoral College to the presidential candidate who receives the most popular votes in all 50 states and the District of Columbia. The bill would reform the Electoral College so that the electoral vote in the Electoral College reflects the choice of the nation's voters for President of the United States. (snip)The website has several links to analyses of the constitutionality of these legislative efforts at the explanation pages.
The shortcomings of the current system stem from the winner-take-all rule (i.e., awarding all of a state’s electoral votes to the candidate who receives the most popular votes in each state).
Because of the winner-take-all rule, a candidate can win the Presidency without winning the most popular votes nationwide. This has occurred in 4 of the nation’s 56 presidential elections. Near-misses have been common. A shift of fewer than 60,000 votes in Ohio in 2004 would have defeated President Bush despite his nationwide lead of 3,500,000 votes.
Another shortcoming of the winner-take-all rule is that presidential candidates have no reason to poll, visit, advertise, or organize in states where they are comfortably ahead or hopelessly behind. In 2008, candidates concentrated over two-thirds of their campaign visits and ad money in just six closely divided "battleground" states. A total of 98% went to just 15 states. In other words, voters in two thirds of the states were essentially spectators to the presidential election.
The U.S. Constitution gives the states exclusive and plenary control over the manner of awarding their electoral votes. The winner-take-all rule is not in the Constitution. It was not the Founder’s choice and was used by only 3 states in the nation’s first presidential election in 1789. Maine and Nebraska currently award electoral votes by congressional district — a reminder that an amendment to the U.S. Constitution is not required to change the way the President is elected.
Among other problems that supporters want addressed, are:
* Candidates ignore states that either seem strongly for them or against them to concentrate on swing states;
* They want to make sure that every voter, no matter where they live, is reached out to, and
* Every voter has an equal say in the electoral outcome. At this time, voters in low population states such as Montana have much more clout than voters in densely populated states such as New York, for instance, on a per capita basis, because of the rule that each state has at least one representative to the electoral college. The voters' say is further diluted by most states' adherence to the "winner take all" rule. States such as Illinois or New York that have high density urban areas that outweigh the large rural areas, for instance, often have strong liberal votes in the urban areas and conservative votes in the rural areas. But the urban areas often have a population density high enough to out-vote the large rural areas of the state. So, the vast swathes of upstate New York and downstate Illinois are outvoted by the urban behemoths of New York City and Chicago, respectively, and because of "winner take all" rules, the conservative rural and suburban voices are drowned out. Only a few states, such as Maine, use different rules, where, in Maine, for instance, each Congressional district elects its own electoral college member.