I'd like to clarify that At-Will is a two way street. Employers can fire at-will as long as it doesn't violate laws like discrimination for race, religion, sex or national origin. But it also means an employee can walk away at any time. With two weeks notice (used to be standard but is becoming rarer), with a days notice or just never comes back from lunch.
And I will also add, as a business owner, that you don't fire someone unless you have cause to. Hiring and training someone takes time. Additionally, in Texas, if you fire someone without following progressive discipline policies you have in place, you will likely be on the hook for unemployment. Which raises your taxes. So it's not a good idea to just tell someone they're fired unless keeping them is a bigger expense and hassle than letting them go.