Update.--The government shutdown of some agencies, like the NPS, includes Websites which requires employees to manage, operate and maintain the Websites, Web pages and servers. They will return when the government is back.
Until further notice, meaning Congress passes a Continuing Resolution (CR) to fund the government while they negotiate new 2014 appropriations bills or a longer CR, Mt. Rainier NP, like all National Parks, Wildlife Refuges, National Monuments, Museums, and other facilities, is closed.
This happened twice in 1995, first for two weeks and then for six weeks. I worked for the USGS then and while I, like all employees, wasn't getting paid, I worked as part of the staff necessary to keep the USGS' satellite realtime data collection system working for water resouces and other data for USGS gages.
You can argue the politics till the cows come home, but it doesn't change the reality of a government shutdown. No wins and the employees get nothing except promises of checks (they're salaried not waged, meaning paid for the year than by the hour) later, but no guarrantees for overtime or other extra pay for those who, like me, worked over 40 hours a week.
It sucks. It's bad politics and it's bad government. And the best we can hope is the elected politicians in Congress come to their senses and pass a clean CR for the President to sign and get the government and employees back to work. That's all it takes.
So, if you're planning a trip to Mt. Rainier NP, you're out of luck until that happens. Just pay attention to the news and then wait a day or so for the NP to open.