Several Welsh Tories have called for changes to Theresa May's Brexit plan after more than a third of Conservative MPs opposed her in a confidence vote.
Mrs May won on Wednesday but while 200 MPs backed her leadership, 117 voted against the PM.
Former Brexit minister David Jones said it was a "difficult outcome" for the prime minister.
But Welsh Secretary Alun Cairns said her critics should give her "space" to come up with a deal MPs can support.
Remainer MP Simon Hart also called on Mrs May's opponents to help the government.
Labour Welsh First Minister Mark Drakeford said Theresa May's credibility was "shot".
He said the PM "should now ask to extend Article 50 and call a general election to bring in a government capable of taking decisions".
Mrs May, who is heading to Brussels on Thursday to meet EU leaders, has faced criticism in her party for the Brexit plan she has negotiated with the remaining 27 states.
Many Brexiteers object to the insurance policy aimed at preventing a hard border on the island of Ireland, known as the backstop, which would be difficult for the UK to unilaterally exit.
In a statement after the vote Theresa May said she wants to "get on with the job" but accepted a "significant" number voted against her.
Before the vote all but one of the eight Welsh Tory MPs said they would back Mrs May in the ballot.
The exception was Clwyd West's David Jones, a former Brexit minister.
"When one is talking about the Brexit process one obviously has got to put country before anything else, and I think that's what I and a large number of colleagues did," he said.
"She has got to have our support now, quite clearly, but she's got to consider how she can take the process forward."
Two Brexiteer MPs who supported Mrs May in the vote - David Davies and Chris Davies - also called for changes.
David Davies, who represents Monmouth, said Mrs May should come back from the EU with a revised plan.
"I hope she will be very clear that, if people are not willing to accept the compromise Brexit she brings back, we need to move immediately to the full Brexit that people voted for."
Chris Davies, MP for Brecon and Radnorshire, said Theresa May "needs to go and spend a bit more time in Europe".
"It's the Europeans now who need to change their minds", he added.
Great to see @theresa_may overwhelmingly winning the vote tonight. Time to get behind our Prime Minister.— Paul Davies AM/AC (@PaulDaviesPembs) December 12, 2018
Montgomeryshire MP Glyn Davies, who supported the PM, told BBC Wales that there were still "major challenges ahead" for her but the result was "better than expected".
"The PM is still facing some serious problems," he said. "She needs to have something to bring the DUP back on board as well as the Tory MPs who voted against her tonight."
Carmarthen West and South Pembrokeshire's Simon Hart said it was "quite a good result" for Theresa May.
"The people who have been plotting against her have now been defeated and, if you like, the challenge has gone back to them," he said.
"Do they want to act responsibly and help the government get Brexit over the line, or do they want to continue to meddle from the side-lines?"
Welsh Secretary Alun Cairns urged Conservatives to give the prime minister a chance, saying she was "trying to respond" to the criticism of her Brexit deal.
"I think that as prime minister she should be rightly given the space in order to come up with a package the majority support in the House of Commons," he told the BBC Radio Wales' Good Morning Wales programme.
Ahead of Mrs May's trip to Brussells, Preseli Pembrokeshire MP Stephen Crabb said: "Let's see if there are any meaningful or significant changes - there's still life in this process yet".
He said the government was operating "on a weekly basis".
"We don't have a clear majority in the House of Commons and we're also deeply divided as this vote demonstrates, so it's really hard," he said.
But he said Mrs May "demonstrates time and time again" that she "cares about the country".
PM’s credibility is shot: remains in office on sufferance with no credibility or authority to speak for the country. PM should now ask to extend Article 50 and call a general election to bring in a government capable of taking decisions.— Prif Weinidog Cymru/First Minister of Wales (@fmwales) December 12, 2018
Away from Westminster, the Welsh Conservative leader in the Welsh Assembly Paul Davies said it was "great to see" Theresa May "overwhelmingly winning the vote tonight".
Plaid Cymru leader Adam Price called for a further referendum on the EU.
"A prime minister without a majority for her defining policy is not a proper prime minister," he said.