President Trump Donald John TrumpBarr criticizes DOJ in speech declaring all agency power 'is invested in the attorney general' Military leaders asked about using heat ray on protesters outside White House: report Powell warns failure to reach COVID-19 deal could 'scar and damage' economy MORE seemed to offer likely incoming House Speaker Nancy Pelosi Nancy PelosiPowell warns failure to reach COVID-19 deal could 'scar and damage' economy Overnight Defense: House to vote on military justice bill spurred by Vanessa Guillén death | Biden courts veterans after Trump's military controversies Intelligence chief says Congress will get some in-person election security briefings MORE (D-Calif.) an olive branch Tuesday, inviting her to make a deal to end the partial government shutdown.

"Border Security and the Wall 'thing' and Shutdown is not where Nancy Pelosi wanted to start her tenure as Speaker! Let’s make a deal?" the president tweeted, without offering any details of what a potential deal would look like or a path forward.

Border Security and the Wall “thing” and Shutdown is not where Nancy Pelosi wanted to start her tenure as Speaker! Let’s make a deal? — Donald J. Trump (@realDonaldTrump) January 1, 2019

The shutdown, now in its 11th day, has left 800,000 federal workers around the country either furloughed or working without pay.

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Pelosi appeared to brush aside Trump's suggestion that she was uncomfortable starting her second speakership in a fierce political battle, and gave little indication she was prepared to compromise.

".@realDonaldTrump has given Democrats a great opportunity to show how we will govern responsibly & quickly pass our plan to end the irresponsible #TrumpShutdown – just the first sign of things to come in our new Democratic Majority committed to working #ForThePeople," she tweeted in response to Trump.

.@realDonaldTrump has given Democrats a great opportunity to show how we will govern responsibly & quickly pass our plan to end the irresponsible #TrumpShutdown – just the first sign of things to come in our new Democratic Majority committed to working #ForThePeople. https://t.co/CGl1euCotB — Nancy Pelosi (@NancyPelosi) January 1, 2019

Funding lapsed for about 25 percent of the government on Dec. 22 as Trump and congressional Democrats clashed over funding for his proposed border wall.

Trump said he would not sign spending bills unless they included $5 billion to fund the wall, while Democrats only offered to extend current levels of border security funding, which includes an annual $1.3 billion for pedestrian fencing.

Democrats said they will introduce two bills to fund the government on Thursday, when they reclaim a majority in the House. One would include six of the remaining seven government spending bills, which would fund the related agencies through the end of the fiscal year. The second would provide a one-month extension for the Department of Homeland Security spending bill, which deals with border security.

Democrats are hoping to pressure Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellSenate Republicans signal openness to working with Biden Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll The Hill's Campaign Report: Biden asks if public can trust vaccine from Trump ahead of Election Day | Oklahoma health officials raised red flags before Trump rally MORE (R-Ky.) to take up the bills, though he said he would not bring any bill to the floor that does not have Trump's support.

Conservatives have scoffed at the Democratic approach, and urged Trump to stick to his position.

“If this is the best effort at compromise that [Democrats] can muster then the partial shutdown will continue weeks not days,” Rep. Mark Meadows Mark Randall MeadowsAmerican Airlines, unions call for six-month extension of government aid McEnany tells CNN reporter to come work at the White House for details on health care plan Trump undercuts GOP, calls for bigger COVID-19 relief package MORE (R-N.C.), the chairman of the conservative House Freedom Caucus, told The Hill this week.

Trump's tweet seeking to make a deal with Pelosi came after the president tweeted a number of attacks against Democrats earlier Tuesday.

— Updated 3:20 p.m.