This post has been updated.

Now that House Democrats have started an inquiry into whether to impeach President Trump, is all hope for legislation such as gun control, trade agreements and prescription drug costs dead?

Not necessarily, but if Wednesday morning’s Trump tweetstorm during House Speaker Nancy Pelosi’s weekly news conference is any indication, it will be tough.

Since she announced the impeachment inquiry last week, Pelosi has encouraged her House caucus to at least try to work with Trump on things like a new trade agreement with Mexico and Canada and prescription drug costs. On the morning before she announced her support for the inquiry, she had a phone call with Trump about gun legislation. She encouraged him to support the House’s already-passed background check bills, according to a source familiar with the call.

“Democrats will continue to advance bold legislation For The People, at the same time as we prayerfully, thoughtfully and somberly pursue the facts and defend the Constitution,” she said in a letter to House Democrats on Monday, specifically citing those two issues.

On Wednesday, Pelosi said in her weekly news conference that she would like to work with Trump on things like trade agreement with Mexico and Canada, which needs a vote in Congress to go into effect. Trump was skeptical in the extreme.

He followed that up by describing Democrats as focusing on impeachment to the exclusion of policy work in even stronger — and more vulgar — terms.

It will take both sides acting in good faith to get bipartisan legislation done. That’s difficult in the best of times in a divided government. We are not in the best of times.

The thing is, Pelosi and Trump have some shared priorities. A background check bill was one of the first things the House passed after Democrats got control. After back-to-back mass shootings this summer, Trump has publicly said he wants to do something on gun safety, though he has vacillated wildly on what that might be. Republicans in Congress are waiting on him to come up with a plan to offer them the political protection they need to pass something.

But after pledging to work with Democrats on gun legislation following public mass shootings in El Paso and Dayton, Ohio, Trump has since pivoted to blaming the impeachment inquiry push for Republican inaction on guns.

“You know, we were working on guns — gun safety,” he said, unprompted, at the United Nations. “They don’t even talk — all they’re talking about is nonsense."

Over the past two months, Republicans have blamed no fewer than five things for inaction on gun legislation following the El Paso mass shooting. (JM Rieger/The Washington Post)

Pelosi and Trump also want to find a way to lower prescription drug costs ahead of the election. And on Tuesday, both sides took the tiniest step forward on that. Top Democratic aides and top White House and Trump administration officials met so Democrats could brief them on a Democratic bill to try to lower drug prices. The Associated Press first reported on the meeting. It sounded like a very cautious testing of the waters for bipartisan negotiation:

“Both sides stressed they were not negotiating during Tuesday’s meeting at the White House, but instead were exchanging information and asking questions. Joe Grogan, a top domestic policy adviser to Trump, called it ‘a very cordial and productive working session.’”

If a prescription drug bill were to move despite everything, it would be a particularly unique nexus of cooperation between Pelosi and Trump. The bill allows the federal government expansive negotiating power on drug prices, something other Republicans would prefer is left to private companies. Trump, the AP reports, has notably not criticized her bill.

But that is all very aspirational. The baseline for compromise between Pelosi and Trump right now comes from finding a way to fund the government next year.

Congress could not come to a bipartisan agreement in time for the new fiscal year, which started Tuesday, so they passed a short-term spending bill to keep the government open close to Thanksgiving. That’s right around the time some House Democrats theorize they could have drawn up articles of impeachment.

Another complicating factor is that Trump is ever anxious to get his border wall built before he is up for reelection. The New York Times on Tuesday published a report that this March, Trump suggested shutting down the entire border and shooting migrants in the legs to slow them down. (The White House did not deny he said this.) He has asked Congress for $5 billion to help build the wall, even as he uses billions of military funds under a national emergency declaration to get it started.

This was already one of the most contentious issues between Trump and Democrats, so showdowns over the border wall are almost certainly going to be heightened by an impeachment inquiry. We have seen what happens when things go really badly between Trump and Pelosi: a 35-day partial government shutdown last December into January.

One option to avoid all that drama even under the umbrella of an impeachment inquiry is to just skip having to do any negotiations. Sen. Richard C. Shelby (R-Ala.) told The Washington Post’s Erica Werner that maybe Congress could just keep passing short-term spending bills if House Democrats and Trump cannot agree on what to spend money on next year.

That would seem like a failure to compromise, since funding the government for a whole year is Congress’s most basic job. But in the middle of a historic impeachment inquiry, nearing an election year where both sides have something at stake, it is possible that avoiding a government shutdown is all the compromise we are going to see.

JM Rieger contributed to this report.