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?"

What do you mean by "anti-US" belief? If that person is saying anything that would be a TARP (Threat Awareness and Reporting Program) you should report it to your security manager and CI if you have any CI stationed there. They can look into determining if they are a security threat.

If they're just being political, tell them not to talk politics at work and find out if there's anything else going on. But perhaps tell the PSG so they can address it as their supervisor and look into it as well.