The best way to battle this problem is to practice with the humble metronome. I've heard every excuse imaginable. "I'm a singer, so its the job of the drummer or bass to keep time" or "I practiced a lot when I was younger, so I don't need to practice like that anymore". The truth is, you're wrong. 5 seconds with a metronome will show you how wrong you are. I'm not trying to call you out here. You're in a loving and safe space. We're all just here to help you through this. I'm certainly as guilty (if not more guilty) as anyone. Trust me.
Recently I stumbled onto a video of Victor Wooten talking about practicing with a metronome. While he may or may not have invented the concept, I'll give him credit for the idea because he was the first person I've ever heard say this. The concept is to start the metronome at a fast speed and play a simple idea at "half speed" of the tempo. For example: I've downloaded an app on my iPhone called Pro Metronome. It's free and works fantastically. Its fastest speed is 240 BPM. So I would practice a lick that I would play as if it was at 120BPM. This gives me every 8th note and make it really easy to feel the beat and play the lick. Once I feel comfortable there, I turn the metronome's speed down to 120 BPM and continue playing at the same speed. This forces me to internalize that beat much more. Once I feel comfortable with that, I turn it down to 60 BPM. At this point, I'm only getting half notes and I'm forced to rely on my own sense of time much more to keep in the pocket. If I speed up or slow down I'll quickly lose that internal pulse. I've notice that as I'm forced to depend on my own sense of time, I end up putting the time in my body more and more. My head starts to bob and my foot starts tapping to help internalize that rhythm. Once I'm comfortable with 60 BPM, I turn it down to 30 BPM (the slowest speed that this metronome app will go).
I dare any of the musicians reading this to try this simple little exercise. I guarantee you'll find it harder than you think it is. You can practice like this with any and EVERY instrument (that includes singers). Practice a bass line, a drum beat, a chord progression, or even scales. I spend an hour, every day, running the pentatonic scale up a down my guitar neck. In time with the metronome. This allows me to see how quickly I can actually play it (accurately) and I can use the aforementioned trick to internalize rhythm while I'm practicing scales. Its an easy exercise that's flexible enough to allow you to work on practically anything and is applicable to every musician (I'm looking at you rappers too).
For more challenges you can try playing a 4/4 rhythm against a 3/4 click or knocking the meter down to 2/2 to get the metronome to play even slower or playing everything a 16th or 8th note later than the metronome's time. The goal here is simply to instill a solid sense of time and to build confidence in your sense of time so that your become less and less dependent on the metronome for time.
Here is the video that inspired this blog. Perhaps seeing a master do the exercise and seeing him make mistakes might encourage you to think about implementing these exercises into your own practice regiment.