Yes, it WILL be an issue, unless you're very, very lucky.
The whole point of a visa is that the government of that country has taken into account who you are and where you are from, and issued a set of days that it's happy for you to be in its country for. Flouting those, due to ignorance, accident, or even (some would say unfairly) conditions out of your control, like flooding or breakdown can cause you to be fined, charged or imprisoned. In most cases, it'll merely be a fine.
In some situations, violating visa rules can cause you to get barred from entering the country again, and if you have to put that on visa applications for other countries can cause you to have restrictions on visas for those.
I've seen people be deported for going to the govt and asking for an extension after theirs was up, and being barred from coming back - we had a police guard at our hostel while his flight was being sorted. I've seen a Canadian marched off the Trans-Siberian because he didn't realise the border crossing was after midnight, and therefore was considered an overstayer. And I was getting very stressed in Uzbekistan when I crossed the border to Tajikistan with 8 hours left on my visa :)
It's one of those rare cases where it's easier (and cheaper) to ask permission than forgiveness. Apply for either a visa extension, or what I did for Tajikistan - apply for a second visa. They didn't mind - just as when you have two trips coming up to a country you may want two visas, I just scheduled the two back-to-back.
It did cause a bit of confusion at the border, but once they worked it out, no problem. And legal confusion is far preferable to illegal overstaying and fines, or worse :/
Some more links of use: