There is no difference between a spam transaction and a non-spam transaction (at least, on a technical level).
If a spammer wants to push up the fees, or fill the blocks with his spam transactions slowing down the confirmation of "normal" transactions, he has to outbid the fee (in sat/byte) of the "normal" transactions.
https://bitcoinfees.earn.com/At this moment, an average sized transaction would need a fee of 0.00064 BTC (about $5 at current preev rate). An "average" blocks contains about 2000 transactions, on average the time between blocks is 10 minutes...
So, in order for a spammer to completely stop all "normal" transactions, he would need to spend 0.00065*2000*6*24 BTC per day in fees.
In total, it would cost 188 BTC/day for a complete attack (about $1.5million at current preev rate). But even in this case: if the user raises his fee to 290 sat/byte, the spam transactions at 280 sat/byte would just sit in the mempool untill all "real" transactions are included into blocks (or untill they're dropped from the mempool).
I wouldn't worry about this... There is no real security thread, it's just a nuicence. You'll either have to wait, temorarry switch to altcoins or use a higher fee untill the spam attack is gone. Spam attacks have been happening many times over the last couple of years, sometimes they last a couple of days/weeks, but they always end eventually.