Bad vibration/rattle under the accelerator?

I have a 2011 Mustang GT with the 6-speed manual transmission. Lately, I've noticed that on a cold start, when I take off in first gear, there is some kind of vibration/rattle under the car that feels like it is close to where the accelerator foot is, almost like something is rubbing bad. This problem is multiplied when making a left turn out of work, but also happens on a straight-away. After the engine warms up, I can't replicate the problem. This is what I'm worried about with taking it to the dealership...they won't be able to reproduce the problem if it is not a good cold start...and I really hate to be without a car for a whole day to let it sit and get cold.

Any suggestions or anyone have this problem?

Thanks,
Austin

UPDATE: I think I used the wrong description of the problem...there is no rattle. There is a bad rubbing sound/feeling when accelerating which is worst at cold starts and sharp turns, but has gotten worse and now occurs even after the engine has warmed up. It's almost a feeling that there is resistance when I go to take off. I'm going to try to get into the dealership Monday, they might just have to let it get cold though and I will just have to wait around because this is my daily driver.

I checked all the exhaust points and everything is tight and stiff...nothing budged when I tried to shake it.