The republican senate and republican house couldn't come up with a compromise spending bill to fund the government. They didn't conference by Sep 30 2013, which caused the government shutdown Oct 1, 2013 (FY 2014)
There was nothing for Obama to sign.
nothing that obama wanted to sign
however he did try to close down Mt Rushmore out of spite
South Dakota footed the bill to keep it open
This is where I have to start calling you idiot names, because you're too stupid to read a history book on the shutdown.
In this case wikipedia.
The deadlock centered on the Continuing Appropriations Resolution, 2014, which was passed by the House of Representatives on September 20, 2013.[12] The Senate stripped the bill of the measures related to the Affordable Care Act, and passed it in revised form on September 27, 2013.[12] The House reinstated the Senate-removed measures, and passed it again in the early morning hours on September 29.[12] The Senate declined to pass the bill with measures to delay the Affordable Care Act, and
the two legislative houses did not develop a compromise bill by the end of September 30, 2013, causing the federal government to shut down due to a lack of appropriated funds at the start of the new 2014 federal fiscal year