I've thought this for a while, and watching Broxton today just solidified my view. Here are their respective 2013 stats:
Jon Broxton
25 games, 23.1 innings, 21 hits, 7 BBs, 15 Ks, 1.20 WHIP, a 5.79 K/9 rate, and a 4.67 ERA.
Sam LeCure
21 games, 23.1 innings, 11 hits, 9 BBs, 25 Ks, .857 WHIP, a 9.6 K/9 rate, and a 1.16 ERA.
It's time for Sam to take over the 8th.