Republicans appealed the ruling of a lower court that chose a map supported by Democrats to redraw the lines.
Oral arguments took place Thursday in Denver.
"Their map is a partisan map and I believe that to my core," said attorney Richard Westfall, who argued against the Democrats' map to the justices.
"I guess I'm off his Christmas card list," quipped Mark Grueskin, an attorney arguing in favor of the map adopted by the lower court.
Westfall argues the map in question ignores decades of precedent and makes too many drastic changes.
The most controversial of those changes are particularly bad for Rep. Mike Coffman (R-Colorado). Under the new map, his district would cover all of Aurora, instead of just the south end, and he would lose a large block of rural area in his district today.
The result would be a shift toward more urban voters, who tend to vote for Democrats.
Aurora argued in favor of the Democrats' map because it wants to be represented by a single district, instead of being split among two districts, like it is today.
Douglas County sided with Republicans, hoping not to be lumped into District 4, which covers the Eastern Plains.
Republicans argue that the people in Douglas County have more in common with voters in metro Denver than they do with rural areas to the east.
"Douglas County is more connected today to the Denver area, not less," Westfall said.
Lawyers supporting the Democrats' map say Douglas County has more in common with the Eastern Plains than might be expected. They point to a common concern about the oil and gas industry and the rise of fracking in Douglas County.
"The [Douglas] County staff said [they] had meetings with hundreds of people who wanted to come talk about it," Grueskin said.
Lawyers fighting the Democrats' map say it's still possible to come up with a different plan by the deadline.
If the high court does throw the Democrats' map out, there are already plenty of other maps to choose from.
(KUSA-TV © 2011 Multimedia Holdings Corporation)