The Republicans will have to win Ohio and Florida to have any chance of winning. The Democrats best chance of winning would be to secure and win Virginia.
Map of red states and blue states in the U.S. based on presidential elections since 2000. Red: The Republican candidate carried the state in all four most recent presidential elections (2000, 2004, 2008, 2012). Pink: The Republican candidate carried the state in three of the four most recent elections. Purple=The Republican candidate and the Democratic candidate each carried the state in two of the four most recent elections. Light blue: The Democratic candidate carried the state in three of the four most recent elections. Dark blue=The Democratic candidate carried the state in all four most recent elections.
If the Republicans are able to hold all of the states that Mitt Romney won in 2010 they would need another 64 votes in the electoral college to win the next presidential election. It would be very difficult for them to do this without winning and adding Florida (29) and Ohio (18) which have a combined 47 electoral votes. This would still only amount to 253 and another 17 would be needed to reach the 270 electoral votes for election. This would require winning 17 votes from three swing states which are Virginia (13), Colorado (9), and Nevada (6) or possibly winning votes from states that have voted just somewhat more Democratic than Republican since 2000, which are New Mexico (5), Iowa(6), and New Hampshire (3). Do the math.
Even if the Republicans were to win Florida and Ohio, the Democrats would still have a very slight demographic advantage if they could win Virginia. Since the election is likely to depend upon these swing states the demographics would give either a center-right or center-left candidate a better chance of winning. Ohio has voted for the victor in every presidential election since 1960.