Sounds like during the Bush administration, a nuclear strike was on the table if things went bad even without the use of WMD's.
No.
The Iraq war ended up being unpopular but it didn't start out that way. Say what you will about Bush but I'm pretty sure one of the only reasons he got involved in Iraq was because he never thought in a million years he would need nukes.
And anyway who would you nuke in Iraq? The massed forces were taken care of in pretty short order. I really haven't analyzed the figures but when it was all said and done I'm pretty sure most of the US troop deaths in Iraq were from suicide bombers, IEDs, and suicides. You really can't nuke your way out of that.
The US has something to lose. If we drop a nuke on anyone we would become an instant pariah state. I don't think any president wants to go down in history has they guy that pushed the button. The same goes for China and Russia. They are not going to drop nukes on anyone let alone us. The Cold War is over.