It stands to reason that if the government shuts down, anything controlled or operated by the government will be affected. Fortunately, a government shutdown would have limited effects on Social Security checks because a shutdown would only affect funds that are annually appropriated by Congress, not those that are sustained by long-term funding.
In the event of a shutdown, most core benefits and programs would continue, including appeals over benefits and disability claims. Where the Department of Veterans Affairs is concerned, Survivor Benefits Plan payments, retiree payments, and VA disability payments would remain unaltered.
In the event that the government does shut down, Social Security checks will be disbursed, but some aspects of the Social Security Administration will suffer. Many employees will be placed on furlough, which means that they will not work or receive pay during the shutdown.
After past shutdowns, Congress has authorized back-pay to furloughed employees. But that does not change the reality that government employees will have to survive without any income until the government reopens.