By Rob Taylor

CANBERRA (Reuters) - A sex scandal rocked on Tuesday Australian Prime Minister Kevin Rudd's scandal-plagued Labor Party in the state of New South Wales -- vital to Rudd's re-election hopes.

New South Wales Labor Health Minister John Della Bosca, a factional heavyweight at state level in the same center-left party as Rudd, quit his post on Monday amid newspaper revelations he had a extramarital affair with a 26-year-old woman.

"I made some poor decisions. You have to take your medicine if you make bad decisions," Della Bosca told reporters on Tuesday.

The state Labor government is deeply unpopular with voters, and opinion polls point to it being thrown out of office in 2011 over a string of scandals and its inability to improve services such as roads, hospitals and schools.

But the state is also a national keystone and with Rudd weighing the possibility of a snap election early next year to overcome an obstructive upper house, Labor's woes there are of deep concern to Rudd and party strategists.

"I don't think there's anyone in the federal government who's going to want to be distracted by anything like this," said Agriculture Minister Tony Burke.

Rudd's government, riding high in opinion polls, controls 83 seats in the 150 seat lower house of parliament. NSW has 13 seats in the national parliament held by tight margins of less 5 percent, many in Sydney's suburbs and fringes.

It is also home to almost a third of Australia's 21 million people and a third of national gross domestic product, valued at A$360 billion ($303.8 billion), despite the highest unemployment record of Australia's six states.

"SPECTACULAR FALL"

The resignation and lurid details of sex in Della Bosca's ministerial office could cement anti-Labor sentiment, leaving Rudd vulnerable to a backlash from frustrated voters in the state in national elections, say political analysts.

"Expect Kevin Rudd to take out an Apprehended Violence Order against the NSW government when campaigning in Sydney," wrote political columnist David Penberthy on The Punch news website, referring to court orders barring contact between defendants.

"Della Bosca's spectacular fall confirms the standing of the NSW Labor government as a cross between the last days of Rome, and Melrose Place," Penberthy said, referring to a U.S. television soap opera.

State Labor leader Nathan Rees was constantly asked by reporters on Tuesday whether he and his government would resign, while the national conservative opposition lawmakers attempted to link the state scandal with Rudd.

"The electors should put this government out of its misery and I'm sure if ... Kevin Rudd were being honest, they would say the best thing Nathan Rees can do for the federal Labor Party would be to quietly disappear," said senior national conservative MP Tony Abbott.

Rudd, speaking in Western Australia, declined to comment on any national implications of the scandal.

"I don't see any point in providing lectures to anybody on this sensitive and delicate matter," he said.

($1=1.185 Australian Dollars)

(Editing by Robert Birsel)