The U.S. Capitol in Washington, DC. Getty Images

President Donald Trump and Congress have until Friday at midnight to dodge a partial government shutdown. But the president and lawmakers appear no closer to breaking an impasse over funding Trump's proposed border wall. A week has passed since Trump said he would be "proud" to close parts of the government during an Oval Office fracas with Democratic congressional leaders Nancy Pelosi and Chuck Schumer. The Democrats say Trump has not responded to their two proposals to keep the seven unfunded U.S. agencies running.

As of Monday night, even Senate Republican leaders did not know the president's plan. They appeared to wait for a signal from Trump — who laid out his case for a wall in a Monday tweet, but did not speak during the day about efforts to strike a deal. "If there's a plan, I think at the moment it's the president and the Democrats trying to figure out what they can agree upon," said Sen. John Thune, a South Dakota Republican and the third ranking GOP senator, according to Politico. He added that "this is going to have to build for a few days here before there's a solution out there." But on Tuesday morning White House press secretary Sarah Huckabee Sanders told Fox News that the administration could support "$1.6 billion for the wall ... as long as we can couple that with other funding resources to get to the $5 billion." She added, "at the end of the day we don't want to shut down the government. We want to shut down the border." WATCH: These virtual walls could be the cheaper and more effective alternative to Trump's $5 billion border wall

Trump has already signed bills into law to fund five government departments, including the sprawling departments of Defense and Health and Human Services. Lawmakers need to fund another seven agencies before the end of Friday. Funding for the Department of Homeland Security, and Trump's wall, have blocked the path to a deal. The immigration dispute raises the specter of the third partial shutdown this year. While damage will be limited because only about a quarter of the government is unfunded, this closure would come only a few days before Christmas and likely last until after Democrats take a House majority in the new Congress on Jan. 3. The impasse casts doubts on Washington's ability to function in the new Congress, where Republicans will hold the Senate and White House and Democrats will control the House. Trump wants Congress to pass $5 billion for the wall, even though he previously insisted Mexico would fund it. Pelosi and Schumer have flatly denied the president's request. They call the proposed barrier inhumane and ineffective. WATCH: Controversial walls in history: From Berlin to the US-Mexico border