Overall opinion of the court is high. There's still a 21 point gap between the favorable and unfavorable rating, but the trend has been downward for 25 years. And Democrats are more likely to support the court than Republicans. The decline among Republicans has been especially severe. Democrats have had a relatively steady opinion of the court since 2008. Republicans responded negatively to the two most recent nominations to the court as well as the decision in the ACA.
Liberals and conservatives might as well be looking at two different institutions based on this data:
Overall the court is seen as being middle of the road, but conservatives think it is liberal and liberals think it is conservative.