"Due to the current lapse in appropriations, IRS operations are limited. However, the underlying tax law remains in effect, and all taxpayers should continue to meet their tax obligations as normal.
"Individuals and businesses should keep filing their tax returns and making deposits with the IRS, as they are required to do so by law. The IRS will accept and process all tax returns with payments, but will be unable to issue refunds during this time." (italics added by me)
As the Journal of Accountancypoints out, "This marked a change from its [the IRS's] shutdown contingency plan, under which 859 employees in its Information Technology Services Enterprise Operations were excepted from the general shutdown furlough to ensure 'refunds continue to process'."
The IRS has not given a reason for its change to also furlough these 859 employees, and to only process tax returns and tax payments, but not tax refunds, during the Government shutdown.