I've imported the datepicker to my Eclipse and I can to build it without any error.
Have you downloaded all the necessary Android SDK files using the Android SDK Manager? I see your 'MainActivity' is having compile error too.
Edit:
From the errors, seems like the attributes buttonBarStyle were only defined starting in API Level 11.
There are a few ways to solve this.
1) Set your app and the library project minSdkVersion in AndroidManifest.xml file to "11", this will make your app not be able to use on older Android versions though.
2) Move this particular layout file to res/layout-v11/ folder, and create another version of the same layout file in res/layout folder, but doesn't use the buttonBarStyle.
3) Seems like there's a way to create a attr.xml file in res/layout, and define the attributes manually. I have not tried it personally though you might want to try.. refer to error: Error: No resource found that matches the given name: attr 'buttonBarButtonStyle'
Good luck
Edit2:
Changing android:minSdkVersion="11" and android:targetSdkVersion="17" in your datetimepicker AndroidManifest.xml file should work!
From your screenshot, I saw that it doesn't recognize "HONEYCOMB", seems like your ADT version is not the latest, please try update it to the latest first.
After that right click your datetimepicker-library project in Eclipse, click 'Properties', then go to 'Android' tab, you should see API 15 or above checked, for mine I have API 17 checked as shown here https://i.stack.imgur.com/3vMk2.png
I think your eclipse is not configured properly