Mr Simpson said a law change would net "not hundreds, but a handful" of drivers each year who evaded court action because of technical problems in extracting blood.
They were mostly people whose intravenous drug use had damaged the vein in their arm, making it more difficult to remove blood.
Police could not extract blood from other veins in the body.
Mr Simpson cited a case in August when a known drug user had his case dismissed by a judge in the Rotorua District Court because police had been unable to take a blood sample.
"As the tourniquet was being put on him by police, he had the gall to say, 'Good luck', to them," Mr Simpson said.
The bill is likely to pass its first reading, expected to be on Wednesday, with the support of the National Party, United Future and the Act Party.
But the legislation has stirred some controversy, with Attorney-General Chris Finlayson flagging it as inconsistent with the Bill of Rights because it limits a person's right to be presumed innocent.
Mr Finlayson said the bill was broad and would capture motorists in a range of situations, such as when they were physiologically incapable of providing blood.
Mr Simpson felt the concerns expressed by the Attorney-General's advisers had been "ill-placed".
He said the police would still have to build a case to the satisfaction of a judge to get a prosecution, and the law change simply ensured that people did not escape criminal responsibility.
The Automobile Association supported the intent of the bill.
AA motoring affairs spokesman Mike Noon said he would ask for the legislation to be refined so that police could not exploit it and bypass the full process for testing drivers for alcohol.
At present the bill said an evidential breath test was admissible as evidence if blood could not be taken "for any reason".
Mr Noon said this needed to be tightened, "otherwise the police could say, 'Sorry, there's no doctor today'."
He said the blood test procedure needed to be simplified. "It takes the doctor 30 minutes, he has to sign his name 17 times, and the form is so old that it's carbon paper."
By the numbers
32,000 people caught driving with excess blood-alcohol level in 2011
10 minutes given to suspected drink-drivers to decide whether they want a blood test
45 minutes for police to process every drink-driver
'a handful' more drink-drivers expected to be convicted by the closing of a loophole in blood-alcohol testing
