The dispute was over whether the Colorado Bureau of Investigation has enough staff to quickly process background checks when people apply for permits. Democrats in the House, along with the CBI, wanted more money for the program. Senate Republicans did not, arguing that wait times are acceptable and that the CBI isn’t being efficient.
Democrats attempted to add extra money for the CBI to a supplemental spending bill that funds several programs in the Department of Public Safety. Senate Republicans stripped that money off, and then refused to allow a conference committee to work out the differences. That put House Democrats in a tough spot: they either had to let the entire bill die, or give up the increased money for background checks. They chose the later.
With that issue settled, there is still at least one more budget showdown in the works. The House and Senate are negotiating over whether to unlock money for a program that allows undocumented immigrants to get driver's licenses.