Social security payments, including Supplemental Security Income (SSI) and benefits for retirement, disability and survivors, continue uninterrupted during government shutdowns.

The government shutdown is poised to become the longest ever this week as the impasse between Democrats and Republicans has dragged into a new month.

Thune, however, pushed back on that dire prediction Tuesday, arguing that the 35-day government shutdown will be a faded memory by next year’s election and that Republicans can run on the accomplishme...