Are there survivor cards that match the miniatures that come with the base game?
In the core game no. Their are some 35 survivor cards, and the only 1 to 1 mini/survivor card is princess the dog.
The reason for this, was the original specs for Zpocalypse where for just 2 survivor miniatures (male and female) copied 4 times, but the kickstarter kept going up and a variety of survivor mini's were produced(each showcases 1 of the more interesting weapons in the game). However said mini's were not intended to match specific survivor cards in any mechanical sense(Mainly just to differentiate the players).
The new Alpha and Beta Team expansions each come with 4 new survivors who do directly relate their Miniature, Survivor & Armory card.