Using position absolute and slightly restructuring the css might work better for you.
Also using <button> instead of <input type="button"> makes life a little easier to style.
I've created an example at codepen for you to see.
HTML:
<div class="container" style="width: 300px">
  <input type="text" class="text_input" />
  <button value="Save" class="btn">CLICK</button>
</div>
<div class="container" style="width: 500px">
  <input type="text" class="text_input" />
  <button value="Save" class="btn">CLICK</button>
</div>
<div class="container" style="width: 200px">
  <input type="text" class="text_input" />
  <button value="Save" class="btn">CLICK</button>
</div>
CSS:
.container {
  position: relative;
  border: 3px solid orange;
  height: 50px;
  overflow: hidden;
  margin-bottom: 10px;
}
.text_input {
  height: 44px;
  width: 60%;
  padding: 0;
  line-height: 30px;
  font-size: 20px;
  padding: 0;
  margin: 3px;
  margin-left: 20px;
  border: none;
}
.text_input:focus {
  outline: none;
}
.btn {
  position: absolute; 
  height: 50px;
  line-height: 50px;
  right: 0;
  top: 0;
  margin: 0;
  padding: 0;
  background: orange;
  color: white;
  border: none;
  width: 30%;
  font-weight: bold;
}
.btn:hover {
  color: black;
  cursor: pointer;
}
Gives you this:

See it working on codepen