President Joe Biden’s meeting Wednesday with Sen. Shelley Moore Capito on infrastructure comes at what Transportation Secretary Pete Buttigieg calls an approaching “fish-or-cut-bait moment” in negotiations with Senate Republicans.

The meeting, the fourth between the administration and the West Virginia Republican, comes just days before work on infrastructure ramps up from high speed to full throttle, with the House Transportation and Infrastructure Committee set to mark up its highway bill June 9. 

The Senate Environment and Public Works Committee approved its draft five-year, $312.4 billion highway bill on May 26, and lawmakers from both chambers say the work being done on those bills will likely serve as the cornerstone of whatever larger infrastructure plan ultimately passes. The two sides are far apart on how much to spend and how to pay for roads, bridges and other traditional infrastructure elements.

Capito has been leading a group of six Senate Republicans hoping to strike a deal with Biden on infrastructure, first trying to push the package from his initial offer of more than $2 trillion to a $568 billion package. When Biden countered with a $1.7 trillion plan, they responded on May 27 with a $928 billion package. 

“We are inching towards one another,” Capito told “Fox News Sunday.” She is the only Senate Republican scheduled to attend the meeting Wednesday.

Capito has emerged as the go-to deal-maker for Senate Republicans in the infrastructure negotiations. As Environment and Public Works ranking member, she’s the party’s top voice on the committee with jurisdiction over highways, which she calls the “anchor” of infrastructure. She says her Republican colleagues need to show they are “for something.”

Buttigieg appeared on several Sunday talk shows and stressed that it’s time for Congress to move forward. He told CNN’s “State of the Union” that by the time Congress returns from the Memorial Day break, on June 7, “we need a clear direction.”

Speaking Tuesday on Air Force One, White House Deputy Press Secretary Karine Jean-Pierre said that while Biden is “appreciative and heartened” by the Republican engagement, “we do need to finish these negotiations soon.” 

“We are working actively with members of the House, of the Senate this week, so that there is a clear direction on how to advance much-needed jobs legislation when Congress resumes legislative business during the week of June 7,” Jean-Pierre said, adding that this week “will be incredibly critical” to the package’s future.

While the topline offers between the administration and Senate Republicans keep moving closer, two key differences — what constitutes infrastructure and how to pay for the bill — remain points of contention.

Capito and the Senate Republicans argue that the bill should focus on “hard” infrastructure, such as road and bridges, waterways, ports, transit, airports and broadband. Biden’s proposal has included senior care, veterans’ hospitals and schools, which Republicans say do not qualify as infrastructure.  The president later proposed a second, $1.8 trillion initiative designed to reduce child poverty, provide for universal pre-kindergarten and two years of tuition-free community college, and paid family and medical leave for workers. 

Speaking on “Fox News Sunday,” Buttigieg defined infrastructure as something that “lets people participate in the economy,” saying Biden’s proposal for $400 billion for home- and community-based elder care would give caregivers the same opportunity to enter the workforce as a new bridge or road might. 

“Americans can’t wait for us to resolve a dorm room debate over which policies belong in which categories,” he said. “They want us to just get it done.”

The two sides also disagree over how to pay for the measure, with Biden calling for undoing some of the 2017 tax cuts and the GOP calling for repurposing unspent COVID-19 relief dollars. The president’s budget request released on May 28 calls for a 28 percent corporate tax rate, but Biden has indicated in public remarks an openness to a rate between 25 and 28 percent, up from the current 21 percent. Republicans have rejected the corporate tax increase as a nonstarter.

Finally, there’s a debate over how much more the package should spend on infrastructure than the federal government ordinarily does in a year. 

Biden’s plan is all new spending, while the most recent GOP plan is $257 billion above the baseline, or the amount the government would normally spend to sustain the current state of federal infrastructure. Democrats argue the plan should be a massive one-time infusion.

“This is a moment for a generational investment in American infrastructure,” Buttigieg said on ABC’s “This Week” on Sunday. “Otherwise, we’d be going to all this trouble, having all these conversations and doing all this work just to stay in 13th place as a country.”

Some Democrats are pushing to bypass Republicans altogether. New York Sen. Kirsten Gillibrand told CNN’s “State of the Union” that “waiting any longer for Republicans to do the right thing is a misstep.”

“I would go forward,” she said Sunday, urging Democrats to pass a bill through the reconciliation process. 

Niels Lesniewski contributed to this report.