Cambridgeshire and Peterborough Combined Authority (CPCC), set up this year, originally estimated annual running costs of about £1.3m.
But the authority's scrutiny committee voted against approving it, with one member asking if recruitment plans were "written on the back of a bus ticket".
CPCC said a reason for the rise was that a new authority was being created.
The authority, created under government devolution plans, intends to employ 15 staff, including newly-created housing, skills and transport director roles all on annual salaries above £100,000.
After Wednesday's decision by the scrutiny committee, the process of recruiting any new staff cannot begin until CPCC has reconsidered its budget, the deadline for which is 31 August.
Labour Cambridge city councillor Dave Baigent, a member of the scrutiny committee, asked of the new jobs: "Were these ideas written down on the back of a bus ticket? Were they discussed with councillors in advance?"
Lucy Nethsinga, a Liberal Democrat county councillor, said she had concerns over how these jobs overlapped with those in county and district councils.
CPCC chief executive Martin Whiteley said: "We, with 15 staff, will be substantially smaller than any other devolved authority in the country.
"I don't envisage us creating a big shiny office. We'll be looking to work flexibly across council offices."

Welsh language minister Alun Davies told AMs it would help efforts to reach that goal stay on the right track.
Targets to meet growing demand for Welsh-speaking teachers and public sector workers will also be set.
Culture committee chairwoman Bethan Jenkins said AMs had been told 70% more Welsh-medium teachers were needed.
Mr Davies responded that around a third of teachers in Wales could speak Welsh, and that the challenge was to see if more of them would be willing to teach through the medium of Welsh.
Earlier this month, Welsh language commissioner Meri Huws called for "radical change" in the education system to ensure all children under the age of seven were "immersed" in Welsh.

The stark prediction is included in a briefing document prepared by the university and obtained by the BBC.
The document also warns of the impact of a "harder" border on staff working at the university's Londonderry campus.
"Should border checkpoints be re-established, this would have an adverse impact on staff mobility," it said.
Two-thirds of UU's staff from the Republic of Ireland work at the Magee campus in Derry.
"There is also some concern that the vote to leave the EU could result in prospective EU students withdrawing their applications," the document continued.
UU had 1,332 EU students in 2015/16 - including 1,206 from the Republic of Ireland - who paid a total of £3.3m in tuition fees.
UU are calling for the government to provide reassurances about the immigration status of EU students and clarification on their tuition fees and access to student loans.
EU students currently pay £3,925 per annum in tuition fees - the same as Northern Irish students.
EU nationals studying now will continue to receive current loans and grants until they finish their course.
However, the document said: "We are currently awaiting confirmation on ongoing arrangements for EU students in Northern Ireland when the UK leaves the EU."
It also estimated that UU's future share of EU research funding would be worth 17m euros every year.
For instance, the university has received almost 10m euros since 2014 from Horizon 2020, an EU research fund.
The document said that further funding of 10.5m euros for 2016/17 from that programme is currently in negotiation.
Horizon 2020 is worth 80bn euros and awards funding for research and innovation.
It is open to UK institutions while the country remains a member of the EU.
The document called for clarification "as to whether UK universities can participate in EU research collaboration and funding programmes after the UK formally leaves the European Union".
"In a context where we planned to double our external EU research grant income this is of grave concern to the university", it said.
Chancellor of the Exchequer Philip Hammond previously said EU-funded projects signed before the Autumn Statement later this year would be guaranteed by the Treasury after the UK leaves the EU.
However, the UU document warned: "There is already substantial anecdotal evidence that UK institutions (including Ulster University) are being asked to leave consortia applying for EU funding."
A new devolved authority has been ordered to review its estimated budget after it rose by £500,000.
[NEXT_CONCEPT]
The Welsh Government will set a "framework" of five-year targets in its attempt to ensure a million people speak Welsh by 2050.
[NEXT_CONCEPT]
Ulster University risks losing some 20m euros (£17.5m) in European Union funding and tuition fees as a result of the Brexit vote, warns a report.