LMH6611 (OpAmp) draws too much current
There appear to be two possible problems with the circuit that could impact performance. Driving one input above it's specified voltage, and open loop operation. Input range is specified to be maximum of 1.2V below the supply rail. Although the output should not roll over with input overdrive it's probably best to avoid the condition, as other unspecified behavior might occur. 

OpAmps aren't really meant to be used open loop. LMH6611 in particular appears to be sensitive even to the choice of feedback resistor value (see datasheet page 22). Since TI doesn't show any internal details, one can only imagine what might be happening with the OpAmp left in an uncontrolled gain state. This would also be a condition to avoid. Try changing the circuit to add a 1kOhm feedback resistor, and keep the input range within spec.

It's hard to imagine any advantage from using a wide band OpAmp in this way, without feedback. Sometimes there can be benefits to use of an OpAmp as a comparator. Usually those situations are having a multichannel OpAmp with an unused channel, and a need for a low performance comparator. Just don't expect much out of an OpAmp when used as a comparator. If a high performance comparator is needed, use a comparator. For a TI part the TLV3501 might work here.