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But any change to the current system at all, short of opening everything up to unlimited money, is likely to diverge from the views of Senate Minority Leader Mitch McConnell (Ky.), one of the strongest opponents of campaign finance reform.
It's unclear whether that difference of opinion would affect Cornyn, who is the only candidate so far for the No. 2 Senate GOP leadership position. Minority Whip Jon Kyl (Ariz.) is retiring at the end of the Congress, and Cornyn has been considered a shoo-in for the job, given his popularity in the Conference and the expectation of gains in November.
Traditionally, the NRSC and Democratic Senatorial Campaign Committee chairmen have enjoyed a significant amount of influence and a common trajectory to leadership if they maintain or win control of the Senate and use the Senators they helped elect to build a coalition of power within the Conference. But that model may be eroding, especially for the GOP.
The McCain-Feingold campaign law limited soft money to the parties, and a series of court decisions in the past few years has amplified the power of outside money. The result has been to legally constrain the party establishment while outside groups have freer rein.
"It certainly takes away some of the power of the NRSC not only [to] pick candidates but also to drive message," former NRSC Executive Director Scott Bensing said of the influx of outside groups.
Bensing noted that the "first evolution" of the NRSC happened in 2003, after McCain-Feingold passed. He said the campaign committee has become "a clearinghouse for best practices, specifically with online campaigns."
"It is more difficult to hold the Senate committee accountable for outcomes, for wins and losses, but I think there are still many ways to hold the committee accountable for how it spent its money, how it distributed its resources," Bensing said.
Cornyn himself said the "broken campaign finance system" has created a "cacophony" of political voices that sometimes drown out that of the NRSC.
It's a thesis that could be tested again soon if outside groups rush to the aid of Rep. Todd Akin, who has featured Cornyn's face in his own against-the-establishment fundraising pleas and whom the NRSC has vowed not to fund in his bid for Missouri's Senate seat.
After winning the primary to take on Sen. Claire McCaskill (D), Akin lost favor after making controversial statements about rape and rape victims.
"It makes it impossible for the candidates or the political parties, for that matter, to control their message because you have so many different people - I mean, if you look at these campaigns, how many different groups are funding those races? And they can't coordinate with the candidates or the party," Cornyn said. "It's this cacophony of just noise. So I think there's a lot we could do to make this a lot simpler, if we would, but the whole idea of trying, in McCain-Feingold, to limit the flow of money into politics, has been an abject failure. The only thing that's happened is that it's become a lot less