Tory Brexiteer Esther McVey has hinted she will back Theresa May's EU deal next week, despite voting against it both times it came to the Commons.
She resigned from cabinet in November over the deal, saying it did not "honour the result of the referendum".
But speaking to Nick Robinson's Political Thinking podcast, she said Leave-backing MPs will "have to think a different way" for the next vote.
She also called for ministers who voted against the government to be sacked.
Ms McVey accused her successor as Work and Pensions Secretary, Amber Rudd, Justice Secretary David Gauke, and Business Secretary Greg Clark of "destroying democracy" and "ripping up the rule books" by defying the three-line whip on votes this week.
Asked by Nick Robinson if MPs like her would "hold their noses and vote" for Mrs May's deal - which is expected to return to the Commons next week - Ms McVey said: "Yes. They will. I don't know what the number is, but they will have to do that if they... want Brexit."
She accused the government of "running down the clock" and said Parliament had "given away all of its leverage" by voting to rule out leaving the EU without a deal.
"The [situation] now is people will have to take a bad deal rather than no deal," she said.
Ms McVey said the prime minister had "broken" her promises to MPs over her red lines and, as a result, "people are going to have to think a different way next week".
She said that although she had decided which way she would vote next week, she would not say.
But pushed further by Nick Robinson, who asked if there was a chance she may be forced to, she said: "Yes."
The Tory MP also criticised her former cabinet colleagues, who had either voted against the government or abstained on votes earlier this week over ruling out a no-deal Brexit.
She said there was an "an emboldened Remain cabinet... who now doesn't even adhere to collective responsibility [and] who can sit as bold as brass on the front bench and not vote with a three-lined whip".
Asked if they should be sacked, Ms McVey said: "Of course you can't stay in a government. You can't rip up the rulebook. You are destroying democracy [and] destroying trust with the public."