The 'flower' spike you see is coming from another plant.
It looks like Plantain and is blending in very well with your coneflower leaves. If you look very closely the leaves are a little different- shape-wise and are ridged/veiny, and the stems are more flat than round.
Here is our page on Plantain so you can compare: 
https://extension.umd.edu/resource/plantain/
We can't see the base of the plants to say for sure but you may   be able to carefully drive a narrow trowel or garden knife straight down near the rosette and rock it enough to pull the weed out. Otherwise you could keep pulling those leaves off over a long period of time to try and tire out the root.
Your coneflower looks stressed but we can't see any major problem. If they are young and establishing (perennials take a good 3 years to really get going) it will be important to keep them well watered, especially in periods like this week with days of very high heat and no rain.


Christine

Thank you!  I grew it from seed last fall, so it is still very young. I will do a better job with watering.

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You're welcome. 
Enjoy the weekend.

After reading this reply, I went outside and verified that my coneflower is, indeed, surrounded by a plantain! I certainly do feel silly! I decided to just go ahead and trim the leaves for now. In the fall, I will dig the plant up and separate the coneflower from the plantain. Thank you very much for your prompt reply !

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You're welcome!