Can a FRCP Rule 11 Motion suffice as a "responsive pleading," or do you have to either (1) answer the complaint; or (2) file a rule 12 motion, to meet the responsive pleading deadline, and then later file a Rule 11 Motion.
You must file either an Answer or a Motion to Dismiss. If the Court were feeling lenient, it might determine that your Rule 11 motion was in effect a Motion to Dismiss, but assuming that the Court would be lenient in that manner would be unwise. You need to file an Answer or a Motion to Dismiss, and then a Rule 11 motion.
Also, filing a Rule 11 motion is usually unwise right at the outset of a lawsuit absent some extremely remarkable circumstances, particularly if you are representing yourself. I would strongly caution against doing so.