By Colin Packham
SYDNEY (Reuters) - Support for Australian Prime Minister Malcolm Turnbull has fallen to its lowest levels since he took office more than a year ago, an opinion poll showed on Monday, potentially loosening his already tenuous grip on power.
Approval ratings for Turnbull had fallen to 46 percent by Nov. 17, the Fairfax poll showed, a fall of 4 percentage points from the previous survey in June.
With support dwindling, Turnbull has sought to demonstrate his leadership by pushing through several laws that were the centerpiece of his narrow election win in July.
However, a hostile upper house Senate, where Turnbull's conservative coalition failed to gain a clear majority, has fought him at every turn. Political commentators have questioned how long he will survive as prime minister.
In the latest blow, Turnbull was forced to accept another compromise legislative deal on Monday, this time with a drastic weakening of a planned tax hike on foreign travelers.
The government had originally planned to make foreign travelers on working holiday visas pay tax of 32.5 percent on every dollar earned.
But fierce opposition from farmers, who said the "backpacker tax" would drain much-needed resources and risk exports, forced Turnbull to reduce the rate by more than half to 15 percent.
"Compromise is a reality in this parliament that we have before us," Senator Fiona Nash, minister for regional development, told reporters in Canberra. "We have an outcome that will deliver for farmers."
Farmers said the higher tax would discourage holiday workers who make up the bulk of fruit pickers at harvest time, threatening an industry that is set for record exports of A$2.27 billion ($1.70 billion) next season.
Demonstrating his roller-coaster performance as leader, Monday's dramatic compromise came only days after he scored a much-needed victory in parliament with the passage of two other controversial bills last week.
However, Turnbull faces an uphill task in introducing another cornerstone piece of legislation aimed at creating a building industry watchdog.
That bill was one of two he used to invoke rarely used powers to dissolve both houses of parliament and call the July election, which he fought on his government's record of economic management.
He has less than a week to push it through before parliament rises for the year.
" ... if Turnbull isn't able to pass the building industry legislation, I expect further poll slides," said Haydon Manning, professor of political science at Flinders University.
($1 = 1.3392 Australian dollars)
(Reporting by Colin Packham; Editing by Paul Tait)