bonnie's right that it's Cumbre Vieja on La Palma that might slide into the Atlantic and trigger a tsunami that would wreck our Atlantic coast (plus a lot of other places).
Twelve years ago the BBC did a TV programme on Cumbre Vieja, which you can watch online in English or Spanish; there are also various links, including a transcript (only available in English):
When El Hierro was first becoming active last year, someone somewhere online postulated that an event on El Hierro (I don't remember if they were thinking landslide or eruption -- in any case, it was one of the dormant volcanoes on the island, not the new baby volcano in the ocean) was likely to send a wave of water not toward us, but in the direction of the unstable part of La Palma. The thought was that activity on El Hierro would trigger the landslide on La Palma which would then send the tsunami our way.
This might be the original Cumbre Vieja academic paper:
Here are some scientists doing experiments to try to cause a tsunami (they couldn't):
And here's a website claiming it won't happen:
This was my favorite La Palma site; it has great maps and diagrams:
Oooh -- this time the QuickTime animations work!