The watchdog is intended to be independent of both the press and the government, a tricky balancing act which officials have tried to perform by setting up a complex membership process involving a board, an appointments committee, and a recognition panel.
Many journalists argue the system still places too much power in the hands of officials, and are instead pressing for a form of self-regulation.
The debate over the relative merits of the two systems has been running for months, but Miller said the government-backed regulator was the one that officials on Britain's Privy Council had chosen. The Privy Council is an interdepartmental body whose roots stretch back to medieval times.
In a nod to concerns expressed by journalists, she said that some of the rules governing the watchdog would be reconsidered although she didn't go into detail.
"We have a once-in-a-generation opportunity to get this right," she told the House of Commons. "We all want it to be the best we can do to give individuals access to redress whilst safeguarding this country's free press, which forms such a vital part of our democracy."
It isn't clear what happens if Britain's media barons decide they still won't accept the watchdog. The Spectator, a right-leaning magazine, said late Tuesday that it was still opposed to any form of government regulation, which it called "deeply illiberal."
Connew said the reaction from others in the British media world should be watched closely.
"What are they going to do if the press says, en masse, 'No deal'?" he said. "The next 48 hours are going to be very interesting."