How do I deal with a leader who is negatively affecting the morale of my troops and myself?

If the squad leader in question is actively disparaging the US as a nation and intentionally de-motivating troops, I would look at SAEDA. Seriously. But that is only if the "leader" in question is deliberately sabotaging the unit. And remember, there is a difference between anti-US and anti-administration or anti-specific policy.

If the individual is actively disparaging elected leaders or the current administration / current policy, remind the individual about rules regarding political speech - i.e. off duty and out of uniform.

If the individual is just a crappy leader who because they suck at leading is a demotivating factor, then you need to have a talk with your troops. Discuss good leaders and bad leaders, and work on building esprit de corps within your small unit. Work on those resilience skills to help deal with Poopy McPoophead and always demonstrate the type of positivity you want your troops to see.

A bit of humor (i.e. Poopy McPoophead) can go a long way to breaking the negativity suck, and if that is coupled with an unrelenting positive attitude from you PLUS an mantra of "we can handle his stupidity together" it will go a long way.

As you grow as a leader, you will realize that half the time, you have to fake it for the sake of your troops. If you just aren't "feeling it" today, it doesn't matter. You have to PRETEND you are feeling it to keep those troops motivated and going. I can't tell you the number of days I cried in my car after PT because EVERYTHING HURT. But I'll be damned if my troops ever saw it.

Could we have more context?
How is that person "anti-U.S.?"
How is that person :actively lowering the morale?"

First, listen to them. Think about this like an NCO. Often, If you have a trooper who is causing problems, one of the first things you do is pay attention to them and see if there is something under the surface that is causing their behavior. So, if it's possible with this person (because I'll admit it is not always possible) try and find some time to talk to them, one and one, and really listen to them. Doing so is crucial if you want them to listen to you and your warnings that they are negatively affecting everyone else.

Second, bring this up to your platoon-sergeant, and possibly the other squad leaders. Let them know what's going on, ask them if they see it too, then ask how you can be help or what the plan is in changing this.

Third, have a talk with the other SPC's. Gauge where everyone is at with this person and if its agreed that they are bringing everyone down, then stage an intervention. It can be as easy as sitting at chow one day and when they start going off, all of you SPCs take a moment to let them know what they do is not appreciated and you would all like it to change. Even if they outrank you, this can be said with tact and respect.

Lastly, use humor. A good ribbing is good for everyone, espeically down-range. Use humor to let them know when they are in the wrong. Don't be a jerk about it. If you do it from a position of truly wanting them to change, then the joke will often come out with the right tone of voice.