Despite a government shutdown in October, visitation at Glacier National Park increased by 1.3% in 2013. During the year, 2,190,375 people visited the park, compared to 2,162,034 in 2012. Moreover, 2013 saw the 4th highest number of visitors in Glacier's history. So who knows, had the park not been closed for two weeks in October, it may have broken its record for the most visitors in one season. Afterall, it was less than 13,500 visitors from that record set in 1983.
Here's a graphical look at visitation counts since Glacier became a national park:
Hiking in Glacier National Park