The National Government has increased health funding annually since first elected in 2008, but critics say it has not kept up with rising healthcare costs and population pressures. Labour says this amounts to a "cut" of $1.7 billion.
This week CTU economist Bill Rosenberg said most of the health budget went to district health boards, whose combined budget required an increase of $551 million to maintain the current level of DHB services.
Dr Coleman has rejected talk of a cut, noting the health budget had increased by $4 billion over the past seven years to a record $15.9 billion.
"Look, the CTU have been running those sorts of arguments for a long time, so I am not at all surprised. But the problem is, they are not focusing on results out of the health system, they think the answer to everything is more money.
"If you look at what has happened in health over the last eight years - more operations, more of everything actually, more of every service. And you would struggle to find a service that hasn't improved."
The Cancer Society has made funding for a national bowel screening programme one of its top wishes for tomorrow's Budget.
This month, Dr Coleman said a business case was still being finalised.
He said he was "working hard to ensure health remains a key priority for this year's Budget".
Green Party health spokesman Kevin Hague said high on his wish list was increased funding for mental health services and support.
There has been one major pre-Budget health announcement - that the Government will boost funding for Pharmac by $124 million over four years.
The Government said DHBs would also give an extra $11 million towards Pharmac's budget next year.
That is likely to lead to Pharmac funding next-generation melanoma drug Opdivo. Other drugs in the funding pipeline include one for hepatitis C infection, and another to treat brain tumours. Funding could kick in as early as July 1.
Last year, the Budget increased funding for DHBs to meet cost pressures and boosted funding for elective (non-urgent) surgeries to ensure National meets its long-running target of having about 4000 more elective surgical operations carried out each year.