The suggested solution to give some of the jobs to Britons came after two days of talks between unions and the refinery owner, Total.
On Wednesday morning, workers heard a proposed deal would see 40 skilled and 20 unskilled jobs being made available to the British workforce.
But our correspondent said they believed the figure was too low, and rejected the deal.
They also demanded proof that the foreign workers being brought in were on the same pay and terms and conditions as their British counterparts.
Total has consistently claimed this is the case, but local workers do not believe it, Danny Savage added.
Unemployed workers and contractors in oil refineries, power stations and nuclear plants have been taking part in protests since last week.
ONE WEEK OF SUPPORT PROTESTS
1-5: Stanlow oil refinery ; Longannet Power Station ; Drax Power Station ; Coryton Refinery ; Langage Power Station 
6-10: Marchwood Power Station ; Fawley Refinery ; Torness Power Station ; Mossmorran chemical plant ; Aberthaw power station 
11-15: South Hook gas terminal ; ICI chemical refinery ; Corus steel plant ; Fiddler's Ferry Power Station ; AES Kilroot Power Station 
16-22: Cockenzie Power Station ; Sellafield nuclear site ; Heysham nuclear power station ; Staythorpe power station ; Didcot Power Station  Grangemouth oil refinery ; St Fergus gas plant 
Union activists have said the issue has been simmering in the industry for years, with British workers being excluded from applying for some jobs.
Work to expand the refinery was sub-contracted by Total's main contractor - engineering firm Jacobs - to an Italian company, IREM, which decided to use its own foreign workforce.
Total insisted it was not discriminating against British workers and that the decision to award the contract was fair.
Unite shop steward Kenny Ward said workers were "determined to achieve a victory at Lindsey because this is where the fight started".
He said people had had enough of employers using "unjust laws" to "pitch one European worker against fellow European workers" in the pursuit of profit.
Derek Simpson, joint general secretary of Unite, told BBC Breakfast that besides this dispute there was a "wider problem" to address.
"Even if this dispute is settled [there is] still a major problem about how these foreign companies, who win contracts and come complete with a workforce, are going to create other difficulties.
"We need to build in some sort of concept that the jobs that are created by these contracts are open to everyone - to foreign and to UK workers.
"It will occur again, and I'm sure it will occur in other countries as well unless there's a realisation that you can't just use the freedom of labour to the exclusion of indigenous labour."
Protesters have vehemently denied the issue is about racism against the foreign workers themselves.
The CBI has backed Total, while Business Secretary Lord Mandelson has said the country should focus on the economics of the recession, not on "the politics of xenophobia".
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