Yes, the end of the federal stimulus program will impact the stock market. The stock market is extremely sensitive to any sort of economic news and ending the stimulus would be big news. The stock market will no go down when the stimulus ends. It will eventually go up again but at least for the short term it will go down.
The federal stimulus program has been propping up the economy for years. To think that the end of the program won't have any effect is a fool's errand. Removing this amount of funds from the marketplace will certainly have consequences, but it will certainly take some time to see what the actual issues will be.
The end of the federal stimulus program will impact the stock market. The end of this program is a necessary step to force the stock market to make it on its' own. The stock market will take a dip when the stimulus program ends, but it will create a path for the stock market to recover and to make real growth.
The fact that the stimulus has lasted this long in the American stock market shows that the government and the Federal Reserve knew that the stimulus was still having a positive effect on the stock market, allowing it to continue to grow slowly. However, now that the stimulus has been removed, the stock market will have a hard time keeping up on its own.