Signing up Bay Staters to Obamacare health plans will cost taxpayers more than ?$1 billion — a “rude awakening” for the next governor, who will likely have to cut services and raise taxes to pay for the bill, according to a bombshell report to be released today by a Boston watchdog group.

“The next governor and Legislature are in for a rude awakening when the bill from the federal government comes due in early 2015,” states the report from the Pioneer Institute, a conservative think tank. “The result will likely be additional cuts to education, transportation, public safety and/or higher taxes to cover the gap.”

The cost to create a working website to sign people up for health plans under the Affordable Care Act — which the state botched and is feverishly trying to relaunch by Nov. 15 — is estimated at ?$616.3 million, according to Joshua Archambault, Pioneer’s health care expert. That includes hefty payments to Optum and hCentive, out-of-state contractors awarded emergency no-bid contracts earlier this year to fix and relaunch the portal.

Read the study: The Undisclosed Cost of Developing an Affordable Care Act State Exchange in Massachusetts

Pioneer also projects that the state will spend $541 million to carry those who couldn’t enroll because of the disastrous website rollout. Those people are receiving temporary Medicaid — basically free premiums operating on a fee-for-service model. Some 285,000 Bay Staters are enrolled in those plans, which have already cost the state about ?$259 million as of August, according to state Health Connector officials.

Archambault projected it will cost an additional $162 million to cover the Medicaid plans between September and January 2015. And $120 million will be needed to pay for the Commonwealth Care program, which the state unexpectedly extended for another year because of the website woes, Archambault said.

“There has never been a moment to step back and say, how much is this costing us,” said Archambault, “because they always just looked at it in little pieces and not in the aggregate.”

But Connector officials disputed the numbers, and Gov. Deval Patrick called the report biased.

“One thing I won’t miss is having to answer spurious charges from the Pioneer Institute based on politics rather than facts,” Patrick said in a statement from London. “The truth is that Massachusetts is still successfully expanding health care and doing so within budget. The philosophical objections to the ACA of this reliable critic don’t change that.”

One Connector official said the report contained “bad math,” arguing much of it was either miscalculated or double-counted. The official pegged the cost of building the site at $254 million but couldn’t provide a total cost to implement Obamacare.

“More people are getting health insurance today in Massachusetts than before the ACA, and that is a good thing,” said Secretary of Administration & Finance Glen Shor.

Archambault dismissed the criticisms as “a bunch of baloney,” noting that many of his calculations, if anything, were overly conservative, and stood behind the $1 billion claim.