Political analysts say a clear victory in the Sarawak state assembly contest for Najib could lead to snap national polls being called this year even though they do not need to be held until mid 2013.
Najib is attempting to woo Sarawak's 900,000 voters following unprecedented gains made by the opposition at the national level in 2008 in which it won a third of parliamentary seats.
Those results forced Najib's predecessor Abdullah Ahmad Badawi to step down.
Najib's foes are aiming for a repeat in Sarawak at the weekend by denying the government a crucial two-thirds majority that effectively allows the Barisan Nasional (BN) to pass legislation without any obstruction.
The BN held 63 of the 71 seats in the Sarawak state assembly before it was dissolved in March, paving the way for this weekend's by-election.
"Our aim is to defeat BN but realistically it will be an uphill task," opposition leader Anwar Ibrahim told AFP.
"We have no access to the media. There is vote-buying, intimidation and we fear vote rigging. If there are free and fair polls, we can defeat the BN," Anwar said.
Jeniri Amir, a political analyst at University Malaysia Sarawak, told AFP that the BN will retain its two-thirds majority but probably lose some of the seats it won in the last state elections, held in 2006.
"This is the most intense (Sarawak) election battle ever for the BN," he said.
Sarawak is endowed with oil, gas and timber but its people including tribal communities are among the poorest in the country and many do not have access to basic infrastructure such as piped water, electricity and healthcare.
Najib, who has been criss-crossing the rugged state by helicopter and meeting voters in the interior, is pinning his reputation on a decisive win.
"The two-thirds target is something that Barisan can achieve. God willing we are on the winning trail," he was quoted as saying by the Star newspaper.
The opposition is aiming much of its campaign at Sarawak's 74 year old chief minister Taib Mahmud, who has been in power for 30 years and is seen as a controversial symbol of BN dominance.
Monash University Malaysia political scientist James Chin said the opposition could win about 20 seats due to voter unhappiness with Taib, who has denied allegations of large-scale corruption involving his family and political allies.
The alleged maltreatment of tribal communities and the exploitation of Sarawak's natural resources during Taib's rule have also been emotive issues in the campaign.
Chin said Najib needs a big win in Sarawak "to carry on the momentum to the next general election, which is expected to be held later this year."
But veteran opposition leader Lim Kit Siang of the Democratic Action Party, which is a member of Anwar's alliance, said there was an appetite for change.
"The wind of change is blowing strong and hard in Sarawak," he said in a statement on Thursday, adding that "there can be no mistaking the deep and powerful yearning of the Sarawakians for political change."