In the next few days, the Late Show with David Letterman will be welcoming two ladies who - for two very different reasons - have a lot at stake.

This coming Monday, New York Senator Hillary Clinton will be making a sit-down appearance with the late night host.  Although visits from the former First Lady are not unusual (she did have a short bit on his return show in January), this particular date comes at a critical time for the presidential hopeful.  The in-studio chat will happen Feb. 4th…one day before the very important Super Tuesday.  Will she be able to sway anyone outside of New York?  Who knows?  But she’ll be sure to keep smiling while trying.  (And just for the record, Sen. Barack Obama also made a recent appearance on the show.  He read Dave’s nightly Top Ten list just last Thursday.)

After the uncomfortable experience Paris Hilton had back in September, you’d think a reunion with Letterman is the last thing she’d want to do.  But camera time is camera time, and you know how much Hilton loves to be in front of one.  Oh - and she has like this movie to promote or something.  (Then again, she did have a perfume that got very little mention the last time she was there.)

In their last meeting, Dave clearly had very little interest - much like the viewers at home - to hear about Paris’ new side projects.  He wanted to talk about her incarceration and wasted very little time making that clear.  Instead of giving him what he wanted (and thereby, making the situation less cringe-inducing), she did her darndest to make him talk about something else.  That’s when Letterman’s needling reached it’s peak.  After insisting she didn’t want to talk about her jail stint anymore, Dave retorted: “This is where you and I are different. Because this is all I want to talk about.”  Cue laughter.

But it seems Letterman hates to make a woman upset, which is why he made a point of making nice with the hotel heiress.  (Either that, or he simply knows a ratings gold mine when he sees one.)  “Dave called me on the phone and apologized. He wrote me a sweet letter and promised he’d be sweet and he really was — I love him,” said Hilton to the New York Post.  Because of his gesture, Paris (in a pre-taped interview) will be seen again this Friday night promoting her new film, The Hottie or the Nottie.

For those who didn’t get around to seeing the now classic interview (or would simply like to relive the good ol’ days), check out the video below: