LONDON — After a failed bid to secure further concessions from European leaders on Brexit, Prime Minister Theresa May returned to Parliament on Monday with little to offer beyond a new date for a vote on the deal outlining how Britain will withdraw from the European Union.

May said parliamentary debate on the deal would resume Jan. 7, with a vote held the following week.

That didn’t satisfy her critics. Opposition Labour party leader Jeremy Corbyn tabled a largely symbolic motion of no confidence in the prime minister, “due to her failure to allow the House of Commons to have a meaningful vote straightaway.”

The motion, directed at May personally, might be embarrassing for her but could not bring down her government. It also doesn’t require the government to allot time to debate it. On Monday it was unclear when or if such a debate would happen.

If a Parliament-wide no-confidence vote went ahead, May would probably win. Brexit hard-liners in her party, as well as the Democratic Unionists of Northern Ireland that prop up her minority government, signaled that they would back the prime minister.

The latest developments come after what was arguably May’s worst week as prime minister.

Last week, Britain’s embattled leader dramatically yanked a parliamentary vote on her Brexit deal, which would have faced a massive defeat. By delaying the showdown, she bought herself time, but she also angered many lawmakers. Her own party triggered a no-confidence vote, which May survived, but more than a third of her fellow Conservatives voted against her, a serious blow to her credibility. May then received a chilly reception in Brussels, where European leaders made clear they weren’t interested in any renegotiation.

With only three months to go before Britain is set to leave the E.U., May is trying to get her deal through the British Parliament. Brexiteers don’t like it because they want a cleaner break with the E.U., and pro-Europeans don’t like it because they think it is inferior to the current arrangement.

If May doesn’t get parliamentary approval, and if nothing else changes, Britain would crash out of the bloc without a deal in March, a scenario that could halt travel and trade and be economically disastrous, at least in the short term.

“I know this is not everyone’s perfect deal; it is a compromise,” May said. “But if we let the perfect be the enemy of the good, then we risk leaving the E.U. with no deal.”

Corbyn accused her of trying to “cynically run down the clock” so as to present Parliament with “two unacceptable outcomes — her deal, or no deal.”

Although the deal is widely unpopular, it still has a chance.

“I’m not saying it’s likely,” said Anand Menon, a professor of European politics at King’s College London, “but it is not inconceivable that her deal passes.”

“The problem with the Brexit vote at the moment is there are too many options — some want ‘no deal,’ some want May’s deal, some want a referendum, others say if I was prime minister I could get a better deal.” But he surmised that Downing Street hopes that, between now and mid-January, lawmakers will coalesce around a few options.He said there were signs that could happen, “as the people running around saying ‘I can get a better deal’ are doing it less than before.”

May also tried to quash the growing calls for a second Brexit referendum.

The odds of a do-over have increased as it became clear that May’s deal lacked parliamentary support. Some May allies see it as a way to achieve a mandate for her vision, although the push has largely come from campaigners who want to remain in the E.U.

Speaking to Parliament on Monday, May rejected the idea of a second vote, saying it would “break faith with the British public” and “further divide our country.”

Meanwhile, some of her cabinet ministers floated the possibility of a series of nonbinding “indicative votes” in Parliament that could help show whether any option — May’s deal, a softer Brexit, no deal, a second referendum — commands a majority.

Amber Rudd, a senior Conservative who backs May’s deal, told the BBC it was important to “find out where the will of Parliament is,” adding that “nothing should be off the table.”