Current Democratic senators and the two independents who caucus with the Democratic party, King and Sanders, received a total of 68,360,484 votes in their respective elections. Current Republican senators received a total of 59,577,911 votes. The data are here: http://loighic.net/senate/senate_116.htm
This is an imperfect measure of the support for the senators in each party because elections in some years will attract more voters than the elections in other years. Also, this is only counting the votes for the winners of each election to the senate. Votes cast for the losing candidate are not counted. Counting all votes cast, or at least all votes cast for major party candidates, might, in principle, give a more accurate picture of total support for each party. That invites problems, however.
In California, both of the current senators, who are Democrats, ran against a candidate from their own party in the general election. Counting the votes for the winner and the loser in those two elections would add almost 10 million votes to the Democratic total. Conversely, not counting those votes (and not having an election with a candidate from each of the two major parties) is probably penalizing Democrats. If each of those general elections had a Democrat competing with a Republican, then, the Republican would, of course, get some number of votes (in the millions), but the Democratic candidate would get most of the votes that she got under the current system plus most of the votes cast for her actual Democratic opponent. There are similarly problematic situations in Alaska and Maine, albeit with many fewer voters at stake.
One solution to this problem (if it really is a problem) is to give each senator a weighted score: his or her total number of votes multiplied by his or her percentage of the vote. This is a measure of the support for each senator that also takes into account how well his or her opponent did—although it doesn’t exactly solve the California problem. In any case, by this measure, Kamala Harris has the highest score: (7,542,759)(61.6%) = 4,646,553.05 followed by Charles Schumer, Dianne Feinstein, Kristen Gillibrand, and Marco Rubio. At the other end of the list, Chris Coons (DE), Mike Rounds (SD), and the two senators representing Alaska, Dan Sullivan and Lisa Murkowski have the lowest scores—in Murkowski’s case, (138,149)(44.4%) = 61,280.13. These are the totals scores for each party by this measure:
weighted score for Democratic senators: 39,754,785.476
weighted score for Republican senators: 32,707,972.484
Since the Democratic senators still have more support, this is probably not especially useful, except to inform us that Republican candidates don’t have more support than Democratic candidates (which could be the case if, say, several of the Democratic senators with large vote totals won by very narrow margins while the Republican senators with large vote totals won by very large margins). Hence, there isn’t hidden support for the Republican party in the vote totals that are given at the top of the page.