Divisions in the Liberal Party threaten to haunt Sussan Ley's fledging leadership as colleagues raise questions about her handling of the demotion of a firebrand senator.

Party insiders say she could have handled the frontbench demotion of Jacinta Nampijinpa Price better, after the Northern Territorian's controversial comments on Indian migrants.

Liberal sources don't expect a challenge in the short term to Ms Ley, who won the leadership after the party's disastrous federal election result in May under Peter Dutton.

Ms Ley dumped Senator Nampijinpa Price, who is popular among conservatives, from her front bench after she failed to declare confidence in her three times during a press conference.

Many in the party consider the senator's comments about Indian migrants last week as having

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