Pressure is building on Centre Alliance's Senator Griff as the government, the big east coast universities and three state universities – Adelaide, Flinders and South Australia – compete for his critical vote in the Senate on Tuesday.

The three state universities are hoping Senator Griff will extract additional assistance for higher education in South Australia, while the big research universities are asking him to take the whole of the sector into account and reject the legislation in the hope it will be rewritten to iron out anomalies and costs to the sector.