Labor has agreed to support a 13 per cent rate for the backpacker tax.
The opposition is due to announce the position on Thursday afternoon.
It also has the backing of crossbench senators Derryn Hinch, Jacqui Lambie and Rod Culleton.
Labor leader Bill Shorten told reporters in Canberra on Thursday his party would support a 13 per cent rate.
"Whilst the prime minister has been on a frolic of finger-pointing and blame-game, Labor has been working to come up with a solution which will end the mess," he said.
"We are prepared to support a 13 per cent backpacker tax from every dollar earned by backpackers."
Watch: One Nation's compromise rate of 15 per cent
The government continues to insist it won't budge on its recommendation for a 15 per cent rate, with Prime Minister Malcolm Turnbull on Thursday morning upping the ante by accusing Labor of favouring rich Europeans over some of the poorest people in Australia's region.
He said the government would refuse to budge from its plan for a 15 per cent tax on working holiday makers despite a last-minute compromise offer of 13 per cent first announced by senators Hinch and Culleton.
If the issue isn't resolved by the time parliament rises for the long summer break on Thursday, the tax rate reverts to 32.5 per cent.
The prime minister said there was a sinister side to Labor's obstinate refusal to accept 15 per cent, the rate paid now by Pacific Islander seasonal workers.
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"Labor want a rich kid from Germany, from Norway, from Sweden to be paying less tax than someone from one of the poorest countries in the world who is sending money back to their village," Mr Turnbull told the Seven Network.
"What kind of values does that represent?"
Treasurer Scott Morrison said the government remains one vote short of a majority to get its 15 per cent backpacker tax through parliament.
Mr Morrison held talks with crossbench senators on Wednesday night and Thursday morning.
He told reporters on Thursday the government had three One Nation senators, three Nick Xenophon Team members and Liberal Democrats senator David Leyonhjelm on board and would not engage in a "game of ping-pong" on further change.
Senator Hinch said he was confident the 13 per cent rate would be passed.
"We can lock it off and they can have the vote," Senator Hinch told Sky News.
"It will pass because I guarantee we'll be with them."
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Farmers have told the Senate cross benchers the issue needs to resolved before parliament rises.
"Otherwise the politicians might have to pick the fruit," National Farmers' Federation president Fiona Simson told ABC TV.
The NFF says its research supports a tax rate between 15 and 19 per cent.
Independent senator Nick Xenophon warns parliament will be a "national laughing stock" if the impasse isn't overcome.
Employment Minister Michaelia Cash is hopeful the government can lock in a deal with the crossbench.
"But again, if we don't, Labor could step in this morning and could work with the government in the national interest," she told the Nine Network.
