Say you were in a battle that you knew you couldn’t win given the rules that were in place. What would you do? If you answered “Why, change the rules at the last minute, of course!”, you may be a House Republican.
There is (or was) a House rule that says if a House bill is brought up for a vote in the Senate twice and is rejected both times any member of the House may call for a straight vote of the corresponding Senate bill. That’s a straightforward enough rule. It keeps things moving and prevents gridlock. But the modus operandi of House Republicans is gridlock so they can’t have that. To prevent the possibility of a vote ever coming up for the Senate bill, on September 30th, mere hours before the government shutdown, House Republicans altered that rule. Instead of allowing any House member to call for a vote, they changed the rule so that only the House Majority Leader can call for a vote. Who is the House Majority Leader you may ask? Why Eric Cantor (R-VA), of course. So there will be no straight vote on the already passed Senate bill to fund the government and the shutdown can last indefinitely.
But yeah, go ahead and blame Democrats for the shutdown.