Should Democrats make a deal with the president on health care?

Twice in the last two days, Democratic leaders on Capitol Hill have sent letters to President Donald Trump laying out their terms for negotiating across the aisle on health care. Yesterday, they said they would only come to the table if the Republicans agreed they were no longer seeking to "repeal" President Obama's signature health care law.

Today, in a second letter, top Democrats from both the House and the Senate said the president needed to stop, in their opinion, actively work to undermine the current law.

"As President, you have a responsibility to protect and sustain the marketplaces and the coverage they provide to so many Americans," Democratic leaders Nancy Pelosi and Chuck Schumer wrote. "It is time to move forward for the American people. Honoring our responsibility to do no harm, we should take this opportunity to continue to lower costs, improve quality, and expand coverage, while continuing to improve the stability of the marketplaces."

Over the weekend, President Donald Trump suggested he may turn to Democrats for to compromise on a new health care reform bill, but this morning during an interview Speaker of the House Paul Ryan said he was not going out of his way to seek bipartisan support. Ryan added that the idea of Trump turning to Democrats, if Republicans could not get to an agreement on their own, worried him.

He said he and Pelosi were on "very different pages."

Democratic strategists also remain unconvinced that President Trump really wants their party's help and that a deal could be reached. The newly elected head of the Democratic National Committee, Tom Perez, was asked this week if he trusted the President's overtures. "I can give you a one word answer: 'no.' I can give you a two word answer: 'hell no,'" the former secretary of labor under Obama said during an interview with the Washington Post.

When asked what specifically Democrats would suggest to improve health care in this country, he went straight to one of the party's boldest reform proposals: a public option.

Progressives, who have a loud voice in the party these days, are arguing that Democrats should start all negotiations by proposing an even farther-reaching policy: a "Medicare-for-all," single-payer type system.

"The point is, let's fight for the ideal and if republicans want a deal, then we will deal with them from there, but we are not going to back ourselves into a corner," Neil Sroka, Communications Director for Democracy for America, told ABC News in an interview this week.

He argued the "old way" that Democrats used to strike deals was by laying out a compromise position to start and letting Republicans "whittle that away to nothing.""It is not our job to help Republicans get out of the mess they created for themselves ... Our job is to do something but we have to have another side that wants to negotiate with us," he added. "Trump actually needs to start looking for ways he can agree with Democrats and so far we have not seen that."

Not all Democrats believe that the party should advocate for such a sweeping reform like Medicare for all.

Neera Tanden, President of the Center for American Progress, said she was also skeptical that the White House was prepared to negotiate. "If you want to negotiate with Democrats, don't send Steve Bannon to the Hill," she said. The controversial Chief Strategist at the White House has been seen on the Hill in meetings several times in the last few weeks discussing health care reform.

Pelosi did send a letter to all House Democrats this week urging input and ideas for ways to improve the current health care system in the county. The letter was titled, "All Hands on Deck - A Call for Suggestions to Improve the Affordable Care Act."

More moderate House Democrats say they turned down an invitation to go to the White House to meet with a staffer on the issue. "With all due respect to the folks there, if that particular staffer wants to meet, come meet with the Blue Dogs here," Rep. Henry Cuellar, (D-Texas), a moderate leader of the Blue Dog Caucus, told ABC.

House Democratic Whip Steny Hoyer, (D-Maryland), said his members did not want to trek down Pennsylvania Avenue to "be a prop." He said he had not heard from the White House yet.

"I think we were for the public option we passed the public option so that everybody will have availability of policy. Republicans have complained that there's only one option in a lot of places so having a public option in a lot of places would be a good option," he added.

ABC News' Ben Siegel contributed to this report