Biden made a $15 federal minimum wage a key part of his economic platform on the campaign trail, and Democrats have pushed to include a minimum wage hike in the President’s American Rescue Plan aid package. But that prospect has proved unpopular with Republicans in a closely divided Senate, making a bipartisan solution unlikely.

Of course, the same could be said for most of the proposed $1.9 trillion behemoth, which has failed to garner any real GOP support amid its budget-busting spending proposals. Democrats are already bracing to push the bill through using the Senate’s filibuster-proof budget reconciliation measure, which would require only a 51-vote simple majority to pass it into law. But it remains unclear whether a minimum wage measure would qualify for budget reconciliation, which can only apply to bills that have a direct impact on federal spending, revenue, or debt. 

Democrats have pointed to a Congressional Budget Office report earlier this month, which spelled out a minimum wage hike’s impact on the federal budget deficit, as proof that such a measure is eligible under budget reconciliation. However, it will ultimately come down to Senate parliamentarian Elizabeth MacDonough, who is tasked with interpreting the Senate’s rules and is expected to issue a decision on the matter at “any moment,” House Speaker Nancy Pelosi (D-Calif.) said Thursday.

But even if Democrats do get the go-ahead from MacDonough, there’s no guarantee that Senate Majority Leader Chuck Schumer (D-N.Y.) will be able to get his entire caucus in line on a $15 minimum wage. Some of the more conservative Democrats in the Senate, including Joe Manchin of West Virginia and Kyrsten Sinema of Arizona, have already expressed reservations, and Schumer will need those members on his side given how the party holds a razor-thin, 50-plus-one-vote majority in the Senate (with Vice President Kamala Harris holding the tie-breaking vote).

Still, a minimum wage hike has emerged as an increasingly bipartisan political position in recent years, with even more conservative states like Florida taking measures to raise their own statewide pay floors. Meanwhile, corporate America is also taking matters into its own hands; on Thursday, Costco became the latest national retailer to increase its own minimum wage for its workers, hiking it to a $16 hourly rate.

These dynamics likely played a factor in two Republican senators, Mitt Romney of Utah and Tom Cotton of Arkansas, pitching a more modest $10 federal minimum wage this week in hopes of finding a compromise with Democrats. But that proposal—which would require employers to use E-Verify technology to prevent them from hiring undocumented immigrant workers—is unlikely to go far in a Democratic-controlled Congress and is already facing a backlash from progressive observers.

According to the left-leaning Economic Policy Institute think tank, the Romney-Cotton plan would leave 27 million fewer American workers with a pay increase in comparison to Democrats’ proposal—with 11 million fewer Black and Hispanic workers and 16 million fewer women benefiting from the GOP plan. What’s more, it would continue the trend that has seen the federal minimum wage steadily decline in recent decades when adjusted for inflation, according to the think tank.

“Romney-Cotton’s $10 target by 2025 is the equivalent of $9.19 per hour in today’s dollars, about 13% less than what the minimum wage was at its high-water mark in 1968,” the EPI’s Ben Zipperer and Daniel Costa wrote in a blog post Wednesday. “It is unconscionable that we should pay the lowest-wage workers today less than what they earned five decades ago, while the economy’s productivity has more than doubled over the last 50 years.”

Given the lack of consensus on the issue, it’s no wonder that Congress hasn’t managed to raise the federal pay floor in 12 years. The coming days will reveal more about the direction of the current minimum wage debate on Capitol Hill—but as the President himself has acknowledged, the politics may just be too difficult to overcome.