gym equipment, heart rate monitors, calorie burn

I've read a lot about gym cardio equipment over-estimating calorie burn. I joined a gym almost 3 months ago and I've been going 3 or 4 times a week, and I only use the cardio machines (elliptical/treadmill). My 'progress' has been limited to within a range of 2 1/2 pounds that I seem to lose and gain back over and over again, so I've finally decided to stop logging my exercise calories and see if that helps me.

I tend to drink a lot of alcohol which is one of the biggest reasons I put on weight, and I'm trying to cut way back now, but since I was sedentary before joining the gym I feel like I should have seen at least a little more progress than this. Also, I'm not great at sticking to my calorie limit (trying for 1200-1400, often times net more like 1500-1600) but most days I should still be in the deficit range.

I don't have a heart rate monitor and I can't afford one at the moment but the machines at my gym have built-in heart rate monitors, so my main question is to anyone who's worn a good quality heart rate monitor in conjunction with testing the ones in the machines. How accurate (or inaccurate) are the built-in monitors?

I'm 23/F and 5'7/148lbs, trying to get down to 130, so I realize I'm not considered overweight and that it's harder when you're only trying to lose a small amount. I always use the setting where I enter my weight into the machine before the workout. Generally the machines tell me that I burn about 100 calories for every 10 minutes I work out.