President Obama campaigned in Michigan with Dem Senate candidate Gary Peters, making the case for a hike in the federal minimum wage to $10.10. Unfortunately, the wrangling in the Senate today suggests the idea is going to die.

Senator Susan Collins has said she’s trying to craft a bipartisan compromise on the minimum wage that could win Republican support — a compromise that would require hiking the minimum wage to an unspecified point below the $10.10 per hour that Obama and Democrats want. Today Harry Reid ruled out the idea, insisting that Dems won’t agree to anything below $10.10.

In truth, it’s hard to see why Democratic leaders would agree to drop the threshold. Indeed, the incentives run the other way right now.

For one thing, Democratic aides point out, the idea of such a compromise may be fanciful. Even if it were possible to win over a few Republicans for a lower raise, you’d probably risk losing at least a few Democrats on the left, putting 60 out of reach (Republicans would still filibuster the proposal).

Indeed, the office of Senator Tom Harkin — the chief proponent of a hike to $10.10 — tells me he’ll oppose any hike short of that. Allison Preiss, a spokesperson for Harkin, emails:

“A $9 minimum wage, put in place over three years, and then indexed to inflation for future years, would lock in a poverty wage for America’s low-wage workers for perpetuity. Chairman Harkin would not support such legislation if it came up for a vote in the Senate.”

Indeed, Dems would probably take a hammering from the left for supporting a lower raise, even as it isn’t every going to become law in any case, since even that wouldn’t pass the House. It’s hard to see House Republicans supporting any minimum wage hike, just as they opposed the unemployment benefits extension after claiming they were open to one, offering one excuse after another for doing so.

Labor is already putting Dems on notice that supporting a smaller hike is unacceptable. Richard Trumka, the head of the AFL-CIO, tells me this in a statement:

“Any proposal to reduce the increase in the minimum wage should be dead on arrival. Anything less than $10.10 an hour traps more people in deeper poverty. It’s economically, politically and morally wrong. Everyone knows that except for a few politicians in Washington.”

Meanwhile, there is no clear evidence any Senate Republicans (aside from Collins) would support even a smaller minimum wage hike, let alone the number of Republicans you would need to pass something. There are probably 54 Dem (and Dem-allied) Senators prepared to support a hike to $10.10; Mark Pryor is the only exception, but Dem aides think he’d support a hike to, say, $9.00. Either way you’d need at least five Republicans. To my knowledge, Collins has not publicly confirmed that any would be willing to join her.

In the end, Dem aides don’t expect the minimum wage hike to get the 60 votes it needs to break the GOP filibuster on the motion to proceed — whatever its size. But even if it did, Republicans would probably come up with procedural reasons for opposing the raise later in the process — whatever its size.