using an article after a conjunction

The second one is better.

Thanks, but are both forms considered correct?

Maybe the first one isn't considered exactly incorrect, but awkward and ugly. There's no need for the second article and native speakers wouldn't insert one there.

Edit: If somone were giving a speech, perhaps a political speech, and really wanted to intensify those adjectives, s/he might choose to add the second article, but that's not normal speech. Or writing.

If you take out the first expression (a daunting), you would say an overwhelming task. The article goes with the word it's modifying; the conjunction isn't relevant. Therefore, the first sentence is correct:

a daunting and an overwhelming task