Taxpayers are finding it difficult to reach IRS staff to comply with the agency’s deadlines, despite needing to meet their tax obligations as the government shutdown drags on.

Some are still receiving automated notices from the Internal Revenue Service that require a response from taxpayers within a certain time frame, several practitioners said.

The best approach for taxpayers is to “do what you’re supposed to do generally and then document, document, document,” said David M. Sams, executive director at The Community Tax Law Project, a nonprofit organization that aids low-income taxpayers in Virginia engaged in disputes with...