Washington (CNN) South Carolina Democrat Jaime Harrison outraised GOP Sen. Lindsey Graham in the first quarter of 2020, according to fundraising reports filed with the Federal Election Commission this week.

Harrison's fundraising underscores the high-profile nature of the race to flip a Republican seat in deep-red South Carolina. Harrison, a former chairman of the state Democratic Party, won early support from prominent party leaders, including former Vice President Joe Biden.

But Harrison faces a tough road in attempting to oust Graham, a three-term senator with close ties to President Donald Trump. The non-partisan Cook Political Report rates the race as "solid" Republican.

"We're so grateful for this outpouring of support from everyday people who are looking for leadership that puts them first," Guy King, communications director for the Harrison campaign, told CNN.