Some proponents of having the Electoral College replaced by a National Popular Vote to elect the President write:

In today’s climate of partisan polarization, the current system shuts out most of the country from meaningful participation by turning naturally “purple” states into simple “red” and “blue.”
The result is a declining number of Americans who matter and a majority who don’t. Youth turnout was fully 17 percent higher in presidential battlegrounds than the rest of the nation in 2004—double the disparity just four years before. The presidential campaigns and their allies spent more money on ads in Florida in the final month of the campaign than their combined spending in 46 other states….Candidates for our one national office should have incentives to speak to everyone, and all Americans should have the power to hold their president accountable. We’re well on our way toward that goal with the Free State Initiative—escaping the shackles of the current bankrupt Electoral College system.

E.J. Dionne, Jr., who supports the idea, explains that the plan is a justifiable circumvention of the Constitutional Amendment process:

Yes, this is an effort to circumvent the cumbersome process of amending the Constitution. That’s the only practical way of moving toward a more democratic system. Because three-quarters of the states have to approve an amendment to the Constitution, only 13 sparsely populated states — overrepresented in the electoral college — could block popular election.

By over representation, Dionne means that Rhode Island, which has 4 electoral votes that are worth around 250,000 people each, has more electoral college power than California, whose 55 electors each represent around 665,000 people. So, yes, on the face of it, Rhode Island’s people have a disproportionate amount of power over the people of California when it comes to electing the President. A fact that some Rhode Island legislators want to “rectify” by introducing National Popular Vote legislation in both the Senate and House.
But should this national popular vote idea take hold, there will undoubtedly be some consequences for small states that the popular vote proponents fail to acknowledge. Dionne attempts to knock down some anti-popular vote arguments

Opponents of popular election invent scary scenarios to continue subjecting our 21st-century nation to a system invented in the far less democratic 18th century. Most frequently, they warn about having to conduct a nationwide recount in a close election.
But direct election of presidents works just fine in France and in Mexico, which managed to get through a divisive, terribly narrow presidential election last year. Are opponents of the popular vote saying our country is less competent at running elections than France or Mexico?

Well, some would say yes.
Yet, as the point is often made, the U.S. is a Republic and the system was designed to work this way such that there are really 50 separate presidential elections every four years. It’s consistent with our Federal system and also in the spirit of the Founders inclination to distrust direct democracy (like it or not). At the heart of that distrust lay an antipathy to “factions.” As Madison wrote in support of the current electoral system:

The influence of factious leaders may kindle a flame within their particular States, but will be unable to spread a general conflagration through the other States. A religious sect may degenerate into a political faction in a part of the Confederacy; but the variety of sects dispersed over the entire face of it must secure the national councils against any danger from that source.

For instance, besides state-centered factions, there was a very real country vs. city dynamic and a wariness against having a disproportionate amount of electoral power–especially when it came to the presidency–in the hands of one or another of these “factions.” The reasoning behind this was that urban and rural people often have very different concerns and priorities. Breaking up the presidential election into separate state elections mitigated against the urban “factions” gaining too much power over the rural–or vice versa–because most states contained both rural and urban “factions.” As such, politicians would be forced to address the needs of both groups.
Popular vote proponents make much of the fact that only certain battleground states get the lion’s share of attention under the current system and smaller or more uncontested states are ignored. By going to a popular vote, they seem to think that the focus away from a few battleground states. There is also a flaw in the logic that argues that small states have too much proportional power yet don’t get enough attention as “battleground states” under the current system. After all, despite all of the apparent electoral power that Rhode Island has over California, the Presidential candidates weren’t exactly streaming into the state in 2003/4, were they? But, proponents would argue, that a national popular vote would make “every vote count” no matter where it is. Well, I wouldn’t bet on it (some would count more often–badump-bum, tip your waitress, please).
Where can candidates get the most bang for their buck (and they’re sure raising the bucks, aren’t they)? In the cities. And while Dionne attempts to discount the shibboleth of a national recount, I wouldn’t be so quick to do so. 3,000 Palm Beach Counties anyone? However, while I do harbor a fear of widespread vote fraud and corruption in the cities, my biggest concern is that candidates will be encouraged to concentrate on places where they are already popular for the sole purpose of cranking up their vote totals.
So while a Democrat could incessantly campaign in Rhode Island to jack up an overall popular vote tally, they would probably acutely focus on bigger population centers like New York, Los Angeles, Chicago, Houston etc.to maximize their turnout and run up their their popular vote tallies. Under a popular vote scheme, they could do that and still get the Rhode Island votes anyway. So where’s the Democrat incentive to visit a small state like li’l Rhody for the sake of marginal popular vote gains when the big numbers can be had in the big cities?
Similarly, a Republican could adopt a similar, more rural strategy in a state like Utah or Wyoming, though it would be a whole lot more work because the population is more dispersed. They still might try it though, or they might try to take the Democrats on, city by city. If this were to happen, then the interests of the rural and suburban citizens could very well fall by the wayside–or at best be of secondary concern–as both political parties sought to tailor their message to the voters who live in large population centers.
What the popular vote movement does is replace one “ignored” population for another, all under the cloak of “equality.” It’s really just an electoral shell-game cloaked in populist rhetoric. There will still be battleground states, they’ll just tend to be the ones that have big cities and big populations.
And maybe that’s exactly the way the popular vote crowd wants it.