WASHINGTON -- Backed by the White House, Democratic and Republican lawmakers dug into a politically fraught search for compromise on immigration Wednesday, seeking to take advantage of a window of opportunity opened by President Donald Trump. They're under pressure to find a breakthrough before a deadline next week that could lead to a government shutdown neither side wants.

Democrats want urgent action to stave off deportation of some 800,000 immigrants currently protected by an Obama-era program called Deferred Action for Childhood Arrivals, or DACA. Trump still wants his border wall, though he's toned down what that means. Conservatives are watching with a wary eye, fearing he will strike a soft compromise that could infuriate their -- and his -- political base heading into this year's elections.

The No. 2 lawmakers of each of Capitol Hill's quadrants of power -- Republicans and Democrats in both House and Senate -- touched gloves Wednesday afternoon, deputized for action at what appears to be a moment of genuine opportunity to break Washington gridlock.

"Everybody wants to find a deal there, myself included," said Republican Rep. Mark Meadows of North Carolina, chairman of the stoutly conservative House Freedom Caucus. "It better be good, because that particular issue is really one of the issues that got this president elected. He can't afford to make a mistake."

The Democrats talk most about DACA, the program protecting immigrants who were brought to the U.S. as children and are now here illegally. Many have only known America as their home and are viewed sympathetically in opinion polls and among most lawmakers.

Meanwhile, Republicans are heartened by an agreement to discuss other issues, such as border security and Trump's long-promised wall, as well as limiting a preferential "chain migration" system that gives advantages to the relatives of legal immigrants.

Trump no longer talks about the "big, beautiful wall" spanning the length of the U.S.-Mexico border, as he did in the election campaign, but he is demanding some elements of it as part of any agreement.

"We need the wall for security, we need the wall for safety, we need the wall for stopping the drugs from pouring in," Trump said Wednesday. "Any solution has to include the wall because without the wall, it all doesn't work."

Inside the Capitol among the GOP rank and file, most seem to be either supportive of the negotiations or taking a wait-and-see approach.