|Emily D: "I'm Nobody"|
You're more likely to qualify for fair use if you reproduce a few lines, rather than the whole poem. Courts frown (with some exceptions) upon taking an entire work ("[it's] sufficient to preclude a finding of fair use," argued Justice Blackmun in his Betamax dissent). Still, if your use is highly transformative, you can overcome this third fair use factor. For example, an entire image, reduced to a thumbnail for search purposes, qualifies as a fair use.
Good news! The good news is that if you use the work after permission was refused, you can still succeed with a fair use defense. The non-good news is that you've alerted the publisher as to your potential use (so much for flying below the radar). It's a close call and practically, it may really boil down to whether the publisher will actually do anything about your use.