WASHINGTON (AP) — Capitol Hill negotiators are hopeful of an agreement as they officially kick off talks on a homeland security spending bill that is trapped in a stalemate over President Donald Trump's long-stalled border wall.

Left on their own, the seasoned House and Senate lawmakers say they could easily reach a border security deal as they have for two years in a row. But whether Trump would sign it is another matter altogether.

Trump has grown impatient and his demands on his U.S.-Mexico border wall have become more insistent even though Democrats took back the House last fall. Democrats remain united against Trump's vision for a massive wall project, yet some are signaling a willingness to deal in the wake of the 35-day partial government shutdown.

"We've consistently said that we do not support a medieval border wall from sea to shining sea," said Rep. Hakim Jeffries of New York, the No. 4 House Democrat. "However, we are able to support fencing where is makes sense, but it should be done in an evidence-based fashion."

"We've come to big agreements before," said the Senate's top Democrat, Chuck Schumer of New York. "What was the common theme? When the president stays out of the negotiations we almost always succeed. When he mixes in, it's a formula for failure. So, I'd ask President Trump, 'Let Congress deal with it on its own.'"

For their part, GOP leaders want to de-escalate the battle over the border wall and suggest they too could be flexible as bargainers seek a bipartisan agreement.

Senate Majority Leader Mitch McConnell, R-Ky., who pressured Trump last week to end the shutdown, warned the president against triggering another shutdown or declaring a national emergency on the Southwest boundary, a move that could let him redirect budget funds to building segments of the wall.

When asked to describe a border security agreement he'd support, McConnell said, "I'm for whatever works that would prevent the level of dysfunction we've seen on full display here the last month and also doesn't bring about a view on the president's part that he needs to declare a national emergency."

A fresh, protracted crisis could make it difficult to tackle other upcoming business such as a deal to prevent automatic budget cuts to the Pentagon and domestic agencies.

The longest shutdown ever was initiated by Trump after Democrats refused his demand for $5.7 billion to build segments of his border wall. Polls show people chiefly blame Trump and Republicans for the shutdown and widely dislike the wall.

The president surrendered last Friday and agreed to reopen government for three weeks so negotiators can seek a border security deal, but with no commitments for wall funds.

House-Senate bargainers plan their first negotiating session Wednesday.

Trump has retreated increasingly from "wall" as it became apparent that he lacked the votes in Congress to win taxpayer financing for the project, which he initially said would be financed by Mexico.

"Inside the meetings we've had, he's said it could be a barrier, it could be a wall," said House Minority Leader Kevin McCarthy, R-Calif. "Because what a barrier does, it's still the same thing. It's the 30-foot steel slat, that's a barrier."

White House spokeswoman Mercedes Schlapp said: "The president has perfectly set this table for the negotiations with Congress. He wants to give Congress one more chance."

Democrats have repeatedly said they wouldn't finance the wall, which House Speaker Nancy Pelosi, D-Calif., has called "immoral." In recent weeks, they've expressed support for fencing or physical barriers but have left ambiguous exactly what they would back. They've said they want to spend money on more border patrol agents and technology like scanning devices and drones.

"What we aren't going to do is use taxpayer money to fund a political applause line," said Rep. Katherine Clark, D-Mass.

McConnell and many GOP lawmakers have long sought to avoid government shutdowns, aware of the tactic's long and consistent history of backfiring badly on whoever sparks one. In the one that just ended, 800,000 federal workers went unpaid for five weeks, countless Americans were denied federal services and mushrooming problems included slowed air travel and delayed IRS refunds.

Members of both parties have opposed Trump declaring an emergency on the Mexican border. They say it would set a dangerous precedent for future presidents who might use the strategy to push agendas that stall in Congress. If Trump issued the declaration, it would trigger near-immediate lawsuits that might block the money anyway.

"There's no appetite for government shutdowns and there's not much appetite for an emergency declaration. For a lot of reasons, our members are very wary of that," said No. 2 Senate GOP leader John Thune of South Dakota.

Interviews with numerous Republican lawmakers showed little taste for a new shutdown.

"Most members, whatever faction in the Republican caucus, would be opposed to a shutdown and would do everything they can to work some kind of deal," said Rep. Mark Walker of North Carolina, a member of House GOP leadership.

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AP Congressional Correspondent Lisa Mascaro and Associated Press writers Matthew Daly and Jill Colvin contributed to this report.