JSFiddle - React, Tailwind, and code Playground

HTML

<div class="container">
     <h2 class="oneline">This is the header that should never wrap and elipse if it doesn't fit</h2>
    <button>Button</button>
</div>
<div class="container">
     <h2 class="oneline">Header</h2>
    <button>Button</button>
</div>

CSS

.container {
    width: 100%;
}
.oneline {
    display: inline-block;
    vertical-align: middle;
    max-width: 80%;
    margin: 0;
    white-space: nowrap;
    overflow: hidden;
    text-overflow: ellipsis;
}