Opposition Leader Tony Abbott has said he'll put a motion of no confidence to the next sittings of the House of Representatives on budget day, May 14.
Mr Wilkie said he had not made a decision on whether he would support the motion.
"I'll weigh up the circumstances, I'll look at the wording of the motion and I'll make a decision at the time," he told the Seven Network on Saturday.
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However, after a week that he described as an "unmitigated disaster" for Labor, marked by failure to pass its media reforms and the aborted leadership coup, Mr Wilkie said the government needed to get its act together.
"I tell you what, if the government doesn't start showing some stability and some competency I think it is going to struggle to get the numbers when that motion of no confidence does come up," he said.
"I'm keeping a very close eye on the government, all the time, but even more so now.
"And I want to see some stability and competence from this point in time."
Other independents Bob Katter and Tony Windsor are also refusing to say whether they would support the no-confidence motion, but Mr Windsor says he'd support Mr Abbott in his push for a vote.
Labor frontbencher Craig Emerson dismissed the suggestion that the government was facing defeat on the budget day confidence motion.
"We will be bringing down a budget that will be unveiled," Mr Emerson told Seven.
"We'll explain where the money is coming from for our big education reforms ... for our National Disability Insurance Scheme, for our economic policies more generally.
"The independents have indicated that they will take us, that is the government, right through to the next election."
Senior Liberal Malcolm Turnbull said the opposition was not asking the independents to hand the coalition power, but for an early election.
"We are not asking to be made the government. We are not asking the independents to a baton change. We're just saying let the people decide," Mr Turnbull told Seven.
