As the partial government shutdown continues into its third week, congressional Democrats are concocting strategies to cajole Republicans into reopening shuttered federal agencies without giving in to President Trump’s demand for border wall funding.

Because Democrats’ powers are limited to their control of the House, their latest plans are mostly about optics devised to put Republicans in uncomfortable positions as Americans increasingly feel the effects of the shutdown.

As all of that is going on back in Washington, Trump will be headed to the southern border on Thursday “to meet with those on the frontlines of the national security and humanitarian crisis,” according to a tweet from White House press secretary Sarah Sanders.

This week, House Democrats will vote on four separate appropriations bills, starting with funding the Treasury Department and the Internal Revenue Service. The longer the shutdown goes, the greater the chance that Americans’ tax refunds will be delayed. The Democrats' gambit here is that Republicans won’t be able to explain to their voters why they couldn’t reopen the IRS to ensure the on-time delivery of refund checks, which is unrelated to the fight over border security.

Meanwhile, in the Senate, some Democrats are floating an idea to block all business until Majority Leader Mitch McConnell (R-Ky.) agrees to take up the House-passed appropriations bills. Sen. Chris Van Hollen (D-Md.) broached the plan that now has support from several prominent Democrats.

The idea, Van Hollen told Washington Post opinion writer Greg Sargent, is gaining traction in the Democratic caucus and from outside groups. The AFL-CIO endorsed it Monday morning. Minority Leader Charles Schumer (D-N.Y.) came out in support of it in the afternoon.

If the entire caucus adopted the strategy as a united front, it could force McConnell’s hand because he’d be unable to get anything else accomplished. This plan would require Democrats to play the kind of hardball more commonly employed by Republicans. It’s unclear whether they have the stomach for it.

But it might be all they’ve got. As of now, McConnell has given no indication that he will bring up the clean funding bills unless Trump indicates he’ll sign them. Remember, though, that before the holidays, McConnell’s Senate overwhelmingly passed a clean spending bill to keep the government running through Feb. 8 but was then rolled by the president, who decided after the fact that he couldn’t support it. McConnell’s spokesman, Don Stewart, told the Fix that without assurance from the president that he’ll sign it, McConnell’s not going to “take shell votes for the sake of shell votes.”

Over the weekend, talks between congressional leaders and the White House remained at a stalemate. Democrats scoffed at the Trump administration’s offer of making the wall out of steel instead of concrete. Administration officials tried to sweeten the deal for Democrats by proposing an additional $800 million to address urgent humanitarian needs at the border.

But it’s going to become increasingly difficult for the White House to defend using key parts of the federal government as a bargaining chip to negotiate complex immigration policy that has evaded Washington for years. Trump’s visit to the border will be a Hail Mary as he tries to convince the American public that holding out for a border wall is worth holding the federal government hostage.

Meanwhile, public opinion of Congress’s handling of the shutdown is abysmal, with just 18 percent of Americans indicating approval. Neither Democrats nor Republicans are faring well in the public’s estimation, but Republicans are viewed more negatively, according to a HuffPost/YouGov poll released recently.