In the modern day a isolated country with no standing army (and no military agreements with other countries with a military) is invaded. The country in question has similar characteristics to Iceland (minus the military defense agreement with the U.S.) This country has no standing army or major paramilitary force that could pose a threat to the invading enemy army and has not for the last one hundred years (unless you take the lightly armed police and coast guard.) Firearm legislation allows for all citizens to be able to own handguns as well as shotguns and rifles, but few do.
Now the invading enemy army...
Where has this army invaded?
Assuming Iceland is our model country, the enemy force has attacked from the western most point.
How large is this enemy force?
Around 20,000 strong (two divisions.) They are mainly infantry armed with AK-74s and russian body armour. They also have a 500 strong logistics and communications brigade and a mobile AA squadron (with a dozen SA-6s.) There is also a small number of armoured personal carriers (APC) and Tanks; probably T-72s and BMP series APCs (up to 50 APCs and 20 tanks.)
How long until they reach the capital (in the east of the country)?
Two weeks at the most, due to rough terrain that bogs-down their wheeled vehicles.
How can a country with no standing army for the last one hundred years mobilize an army?
Additional Question - Would the defending country's government be able to appeal to the UN or NATO for support/an expeditionary force?