Sen. Bernie Sanders (I-Vt.) confers with Democratic senators from the Veterans Affairs Committee prior to a news conference at the Capitol last Thursday. (Win McNamee/Getty Images)

If they can't do it this week, can they do it at all?

That's what many Americans might be thinking in the next few days as the House and Senate try — or at least appear to be trying — to complete work on a series of complex issues before fleeing Washington for five weeks of campaigning, constituent town hall meetings or overseas taxpayer-funded "fact-finding" missions to swanky corners of Europe.

There are just four "legislative days" left for Congress until a five-week recess begins, and it seemed to suddenly dawn on lawmakers late last week that failing to enact new legislation on a series of complex issues might not sit well with the general public. Over the weekend, several lawmakers tried sympathizing with the frustrated electorate.

"It should embarrass all of us," Sen. Ted Cruz (R-Tex.) told NBC's "Meet the Press." On the same program, Rep. Paul Ryan (R-Wis.) said "Trust me, we're frustrated as much as you are."

By law — yes, really, by law — Congress has to adjourn for the month of August, but that doesn't mean they can't agree to come back and finish their work. Last week more than 100 House lawmakers cosigned a letter to Senate Majority Leader Harry M. Reid (D-Nev.) and House Speaker John A. Boehner (R-Ohio) suggesting that Congress should stay in session until it completes work on legislation to overhaul the nation's medical system for military veterans.

Now, they might not have to. Word came late Sunday that negotiators have reached a tentative agreement that should allow the House and Senate to quickly approve a major overhaul of the Veterans Affairs Department. Sen. Bernard Sanders (I-Vt.) and Rep. Jeff Miller (R-Va.), who chair the Senate and House Veterans' Affairs committees, plan to outline their plan Monday afternoon. Copies of a draft agreement provided by congressional aides suggest that the measure hews more to the agreement passed by the Senate last month with 93 votes — an unheard of tally in the modern age.

The big unknown is whether Miller will be able to convince more fiscally conservative colleagues to hold their nose and approve more than $15 billion in emergency funding for the VA. (But if they don't, it's a safe bet that Democrats will produce campaign TV ads that say something like, "Your Republican lawmaker voted against helping military veterans.") As part of the deal, Republicans pushing for privatization of veterans' medical care will be able to say that they can now seek private care if government-run hospitals and clinics can't treat them within 30 days.

As Congress approves changes to the VA, the department is also expected to have a new leader by the end of the week. Senators are expected to easily confirm former Proctor & Gamble executive Robert McDonald as the next veterans affairs secretary. Each VA secretary has been confirmed unanimously since the post was created in the late 1980s.

So with veterans' health-care out of the way, what's left?

Sen. Bernie Sanders (I-Vt.), and Rep. Jeff Miller (R-Fla.), held a news conference on Monday to announce they had reached a bipartisan deal to fund measures to fix the Department of Veterans Affairs. (Associated Press)

First, federal funding for major road construction projects -- another must-pass as Americans hit the roads for summer vacations. The Senate is scheduled to take up a House-passed measure that would replenish the federal highway trust fund through next May — a nine-month extension that will coincide with the deadline to raise the federal debt limit. Before the Senate gives final approval to the deal, expect votes on at least four amendments — including some that would shorten the length of the deal in order to force debate on a longer-term deal before the end of the calendar year.

If the Senate can successfully pass the measure with minor changes, it should head back to the House for last-minute approval.

Then there's the border.

Salvadorian immigrant Stefany Marjorie, 8, holds her doll Rodrigo while in Mission, Tex. (John Moore/Getty Images)

With a historic number of illegal immigrants streaming across the southern border, the House and Senate are expected to pass competing measures this week that would provide some, but not all of the $3.7 billion in emergency funding that President Obama has requested to deal with the crisis. The House plan is expected to cost about $1 billion and would come with strings attached -- changes to a 2008 anti-trafficking law that would require the Obama administration to more quickly process and deport most of the younger Central American immigrants as quickly as Mexicans are sent home.

But that deal is a no-go for most congressional Democrats, who say that such changes would only endanger children escaping drug-fueled violence in their home countries. Senate Democrats are instead expected to try approving about $2.5 billion in emergency funding with no changes in current immigration policy.

Differences on price and policy make it difficult to see how negotiators would quickly reach a deal by Thursday night when both chambers are expected to adjourn. That would mean a significant cash shortfall for the departments of Homeland Security, Justice and Health and Human Services as they continue dealing with the immigrant influx.

But the impasse should create political opportunities for both parties over the five-week break, with each party able to blame the other for failing to compromise and quickly help address the issue. When asked about top priorities, Americans are increasingly ranking immigration higher than other priorities, including the economy and jobs, meaning both parties might be able to make some gains over the break.

Finally, as Congress gets ready to leave, one top leader prepares to step down. This is the last week that Rep. Eric Cantor (R-Va.) will control the House calendar as majority leader. After stunning the political world by losing his GOP primary last month, Cantor will step down and make way for his close friend, Rep. Kevin McCarthy (R-Calif.). Rep. Steve Scalise (R-La.) — who on Sunday didn't rule out the possibility Sunday of impeaching Obama — will become House majority whip.

Cantor plans to serve out his term as a Richmond-area lawmaker until early January. His last act as majority leader will be to call a vote authorizing the House to file a lawsuit challenging Obama's use of executive orders to tweak the Affordable Care Act. Expect to hear Republicans talk early and often about their plans for a lawsuit back home during the recess.