Start with checking the fuel pressure regulator. With the engine off, pull the vacuum hose off and smell for gas in the hose. If you smell gas, replace the FPR. With the engine running pull the vacuum hose, plug the end of the hose by holding your finger over it (to stop the vacuum leak) and see if there is an increase in idle speed when you pull the hose off.
The symptoms sound exactly like a plugged fuel filter. If you haven't changed it recently, change it.
Check fuel pressure using a gage. You can usually borrow these from most automotive parts stores. You pay a deposit that is refunded when you return the tool.
Is the check engine light on and/or flashing? If so, have the car scanned for diagnostic trouble codes and report back with the findings. Autozone will do this for free.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)