I found seats departing Los Angeles LAX on Friday, January 25, returning from Las Vegas LAS on Monday, January 28.
Other travel dates are also available for weekend travel through March, departing on Fridays, and returning on Mondays. There are slightly lower fares for mid-week travel, but it's always easier to get away for a quick weekend than flying during the middle of the week.
This is a Basic Economy fare, which has strict restrictions on United and is similar to Spirit in that this price only includes a small personal item and advanced seat selection is not included. Spirit does have slightly lower weekend fares, but you still may prefer the onboard experience on United.
A checked bag costs $30 each way for both Basic and standard Economy, but if you only need to bring a larger carry-on bag, opt to pay for the standard Economy fare, which is also an additional $30 each way, and includes a normal sized carry-on bag, standard seat selection, and is eligible for upgrades/ticket changes.
Need a room in Vegas? Here's what's available for the mentioned weekend dates on Hotelwatchdog.