No, there's not a legal limit. However, TSA does recommend that you ask to be screened in private if you're carrying a lot of currency or other valuables in order to prevent drawing attention to items that could be stolen. This is probably good advice since you are separated from your luggage for a bit at the checkpoint, especially if you get stuck waiting in a slower-than-normal line for the scanner after placing your baggage on the conveyor.
I've heard that the United States government can and is seizing any amount of cash over a certain dollar amount at airports.
That is definitely not true. They may be curious why you're carrying $30k in cash and may ask you about it, but they will not (and, legally, can not) seize it unless they have probable cause to believe that you have committed or are about to commit a crime and that said cash is reasonably likely to be evidence of said crime. If they do have probable cause to suspect a crime, then they can refer the matter to law enforcement and keep you around until law enforcement gets there to question you. From the TSA Management Directive copied into page 19 of this legal proceedings document:
When currency appears to be indicative of criminal activity, TSA may report the matter to the appropriate authorities. For all flights, factors indicating that cash is related to criminal activity include the quantity, packaging, circumstances of discovery, or method by which the cash is carried, including concealment... TSA may also note any factors related to criminal activity for purposes of notifying CBP [for international passengers] and/or law enforcement, as well as request that the individual remain accessible pursuant to such notification.
Of course the best advice is probably to simply not carry large amounts of currency with you when you fly in the first place. If you carry it on, it could be stolen at the checkpoint either by a TSA agent or by another passenger. TSA doesn't keep track of whose bag is whose when they go through the conveyor. If someone grabs your bag or takes something out of it before you clear the scanner, they aren't going to know that the bag doesn't belong to that person until it's too late. For checked luggage, you are separated from it from the time you check in until you get to the baggage carousel at your destination. Airline agents, TSA agents, baggage handlers, ground crew, etc. at each airport you transit have access to your bags when you can't see them, so it would be nearly impossible for you to catch the culprit if someone decided to help themselves to some cash.