I admit to not being very familiar with the current state of affairs in the EU. However, if you're referring to groups resistant to increases in federal power in the early US, then yes, absolutely. This was a major issue during the Constitutional Convention and the early years of American politics. One of the two major political parties at the time was the Federalist party, those in favor of increasing the centralized power of the federal government and the remaining party explicitly opposed increased federal power, feeling more should be left to the states to decide.

As initially set up, the states were essentially several independent republics that had united in order to defeat a greater enemy. Once the war was over, the question of how strong the union should remain or even if it should exist came up. There were those on both sides of the issue. The weaknesses in the Articles of Confederation were exposed in the early years following the Revolution through several different means. Goods were taxed variously as they crossed state lines, different states coined different money that other states wouldn't accept, some states wanted to control things like waterways to enforce their power on the others. So, they decided to call a convention to deal with these matters.

The members of the convention weren't of like mind, some wanted more federal power, some wanted less. The desires of a large slave-owning state like Virginia did not match those of smaller free states, so any agreement was going to be problematic. Shortly before the delegates met, a group of Revolutionary War veterans mounted an armed uprising due to financial troubles and were not far from taking over Massachusetts until a partly-privately-funded army was able to stop them. It showed the weakness of a federal government with little ability to levy taxes or raise an army and made many people rethink the need for a stronger federal government. The debate between what powers the states should have versus what powers the federal government should have went back and forth over the summer of 1787, until the Constitution was finally hashed out.

In the years immediately following, the Federalist Party was a dominant political party in the US until it began to lose ground around the turn of the century and completely ceased to exist a couple of decades later.

Hopefully that helped and that was what you were asking.

edit: I changed a word.