The election of 1848 was open after Polk kept his promise not to re-seek office after just one-term. Zachary Taylor was the war hero and general during the Mexican-American war, and was sought out by both parties to run. The Whigs managed to get him to come their side.
The Democrats nominated Lewis Cass, a senator from Michigan.
Former President Martin Van Buren was at it again, and sought another term. Except this time he ran on a 3rd party ticket. He ran on the Free Soil platform which opposed slavery in the expanding west.
Also to note is that Van Buren's running mate was Charles Francis Adams who was the grandson of John Adams, and son of John Quincey Adams. The Free Soil party received no electoral votes.
The Whigs and Democrats attacked each other with the same old rhetoric since this was an open election. It's hard to verbally-attack a president that's not running again. However Taylor's popularity as a war hero gave him a victory over Cass. Taylor beat Cass 163-127 with them winning 15 states each. Taylor managed to get the ones that were worth more.