SJ,
In the widgets css style.css there is this css rule of the header:
.jimu-widget-nearme .esriCTSearchHeader
{
padding: 0px 0px 10px 0px;
white-space: nowrap;
overflow: hidden;
text-overflow: ellipsis;
font-size: 12px;
color: #000000;
font-weight: normal;
}
Line 4 is the part that prevent word wrapping. Try changing that to normal or pre