"Not Today Satan" is a common phrase used by religious people that means "I'm not going to brought down today". While there is clearly an effort to make it out as if Rep. Omar is saying that America is Satan, that is clearly not what this phrase means.
If you look for other tweets that use that hashtag, once you scroll down past the manufactured right-wing outrage, you'll see tweets like:
work drags lol #nottodaysatan
Almost accidentally read an Endgame spoiler #NOTTODAYSATAN
When life isn't the way you hoped, you change it and make it what you need. Work is hard, but providing for myself and my husband is more important than the trivial bitches. #nottodaysatan pic.twitter.com/3i39KznNIW
when I was 14 they predicted a valve replacement at 30. Today was my annual check up, and a bitch gets to keep her valve! What’s good heart disease!? #nottodaysatan
Already know some type of blessing is on the way when the energy vampire ex pops up. Demons can smell happiness. #Nottodaysatan 🙅🏽♀️
No Anti-American sentiment there!
Some more evidence that this is not some sort of secret terrorist hashtag:
As for why she might have said that, the tweet you linked to is a direct reply to another tweet by @j_w_84 which I've reproduced below:
In that tweet, Joshua claims that the that the worst terrorist attack in Somalia was the Battle of Mogadishu where 19 Americans were killed, not the then recent terrorist attack (referenced in the original tweet by Al Franken) where 230 Somalis were killed. The only way that makes sense is if you completely devalue the lives of Somalis, both those killed in the recent terrorist attack (to say that 19 dead is worse than 230 dead) and those killed in the fighting in Mogadishu (U.S. special representative to Somalia Robert B. Oakley estimated that there were 1500-2000 civilian casualties due to the reality of fighting a pitched battle in a crowded city).
It's this casually racist attitude from Joshua, which holds that only American lives matter, that Rep. Omar is referring to: just like heart disease, boring work, or Avengers spoilers, the racist attitudes of some will not bring her down and stop the important work of fighting against it.