Outspoken Tasmanian Jacqui Lambie is set to return to the Senate, but mining magnate Clive Palmer's $80 million political comeback bid appears to have failed.

The Morrison government is not expected to form a majority in the next Senate but will likely be dealing with a six-member crossbench smaller and less ideologically disparate than the last.

Jacqui Lambie looks set to return to the Senate after being forced to resign from Parliament over dual-citizenship concerns. Credit:AAP

With about half the Senate vote counted on Sunday, the Coalition appeared on track for about 34 upper house seats – short of the 39 seats it needs to seize outright control.

Labor and the Greens look likely to hold about 36 seats between them, meaning if those two parties voted as a bloc, the Coalition would be forced to negotiate with the crossbench to pass measures such as its $158 billion income tax relief plan.