How long do clips have to be before I can make transitions longer than 1:00?

Media Handles are required.

Try a test with two clips:

Make an in point two seconds from the start and an out point 2 seconds from the end of each clip.

Place the two clips in the Timeline then add a two second cross dissolve.

Should work.

FCP X can also let you know if there are no media handles and ask if you want a transition at the expense of shortening clips.

Al

Alchroma has already given you the answer - you need handles.

It is not the length of the clips that matter - they can be one hour long, or 5 seconds.

Handles are the extra frames that you are not using. If you select an entire clip in the browser and drag it to the timeline, you'll have no handles.

One way to better understand this is to double-click the edit point in the timeline.

This will open what is called the "precision editor". It will look like this:

Handles are necessary to maintain the length of your edit - e.g. for a 1 second transition you will need 0.5 second on each side of the edit point. These extra frames are combined with the end or start of the other clip to create the transition.

You can set a default transition length up to 10 seconds in Preferences (last line of Editing pane):

so that when you apply a Transition to your clips, FCPX will create the needed amount of media if there are no handles, or use as much as specified.

Otherwise, you can use the tools (essentially hidden) in the Timeline. There are two methods.

The "grab bars" (white arrows) on either top end of the transition can be click-dragged to create more media handle. Drag the right side left and the left side right. After, you can click-drag the transition ends (green arrows) to extend the length of the transition (as far as I can tell, you can make transitions as long as you have media handles... I was able to easily do over a minute in tests... ran out of media length.) The "bowtie" icon (red arrow) lets you perform a roll edit on the media in (under?) the transition.

The second method gives you more precision and it's called: The Precision Editor... Double click on the "bowtie" icon in the transition to open up the Precision Editor. You can perform the same functions detailed above, plus you can click on the clips on either side and drag them (as you do, you get a two-up display to "calibrate" the transition. You can skim the ingoing and outgoing clips and click on a point you want to make the starting IN point and ending OUT point. Etc... It's cool. You should play with it a little to get a feel for it.