Following a five-week vacation from Washington, members of Congress will return to Capitol Hill for a few days starting Monday to hammer out the year’s budget before heading back out on the campaign trail through Election Day.

Their 13 working days in the nation’s capital will be dominated by ugly messaging bills that could threaten a government shutdown. 

Both the House and the Senate will reconvene Monday after members have spent most of August fundraising, marching in local parades, or spending time on vacation with their families. After that break, leadership now sees the work period as an opportunity to force vulnerable lawmakers seeking re-election to take tough votes. 

The most controversial bill that is nearly guaranteed to receive a vote is Congressman Chip Roy’s Safeguard American Voter Eligibility Act. The bill would require voters to provide proof of citizenship when registering to vote in federal elections. Current federal law only requires that applicants swear under penalty of perjury that they are citizens. 

“Every state ought to be very clear that we’re going to force that only citizens are voting in our state, local, and federal elections. But the SAVE Act is meant to layer on top of that, to say that no matter what you want to do at the state and local level, only citizens are going to vote for our Congress, Senate, and President,” Mr. Roy said Tuesday on “War Room,” hosted by a former adviser to President Trump, Steve Bannon.

Speaker Johnson has said that he plans to hammer out a funding deal, known as a continuing resolution, with the Senate that lowers some federal spending, and that he will then attach Mr. Roy’s bill to the House version of the legislation and force the Senate to act. Vulnerable Senate Democrats seeking re-election, such as Senators Brown, Tester, Rosen, and Baldwin, could be key to forcing Senator Schumer to put Mr. Roy’s bill on the floor under that scenario. 

Mr. Roy says it will be a “fight” to get his bill to President Biden’s desk, but it is a fight worth having. Trump said on Truth Social that “Republicans must pass the Save Act, or go home and cry yourself to sleep.”

Spokesmen for several Democratic senators did not immediately respond to a request for comment about the bill.

Not all House Republicans believe that Mr. Roy’s bill should receive a vote before the House leaves town again at the end of September, however. The House already passed the bill in July, with just five Democrats and all Republicans voting for the measure. One hard-right Freedom Caucus member, Congressman Matt Rosendale, says that to put the bill on the floor again or to attach it to funding legislation that will be sent to the Senate is nothing more than Washington lawmakers playing games with their constituents. He says he did not come to Capitol Hill to pass “messaging bills” meant to put legislators in tough spots, but rather to find real solutions. 

“Explain to me how in the world — by attaching [the bill] to a continuing resolution — now it’s now gonna have more likelihood of being passed,” Mr. Rosendale, who voted for the bill in July, told Newsmax on Tuesday. “All this is is a messaging technique and tactic that people want to use. I wasn’t sent to Washington to deliver messaging bills. I was sent to Washington to make changes and make life better for the people of Montana.”

“It’s not going to get passed. It’s disingenuous and it’s dishonest to even attach it,” he added. 

Mr. Schumer, for his part, has also learned the art of forcing vulnerable lawmakers to take tough votes. Just before the upper chamber left for the summer, he brought up two votes that have now been used as hits against Senator Vance in his campaign for the vice presidency. The first was a bill to protect access to in vitro fertilization, which Mr. Vance opposed, and the other was an expanded child tax credit that the Ohio senator says he supports — but when the vote was called, he failed to show up. 

“JD Vance was a no-show on the vote for my bill to expand the child tax credit when it was on the senate floor two weeks ago. My bill failed after Republicans blocked it, leaving 16 million kids worse off,” the chairman of the Finance Committee, Senator Wyden, said in a statement on X.