SENATE MOVES CLOSER TO APPROVING TAX DEAL…. The Senate’s goal today was reaching 60 votes on the tax deal struck by the White House and congressional Republicans. That turned out to be fairly easy.

The Senate on Monday advanced the tax-cut package agreed to between President Obama and congressional Republicans, virtually assuring that the Senate will approve the bill on Tuesday and send it to the House ,where Democrats are threatening to make changes to a provision granting a generous tax exemption to wealthy estates.

The vote in the Senate was not finished, but shortly after 4 p.m. the tally showed more than 60 senators agreeing to end debate, cut off any filibuster and move to a vote on passage.

The vote was 61 to 7, with a whole lot of senators still returning from their home states this afternoon. The leadership agreed, without GOP opposition, to hold the vote open to allow members more time to reach the floor.

The only Republican to oppose the measure, at least so far, is Sen. John Ensign (R-Nev.). Everyone else is from the Democratic caucus, including Vermont’s Bernie Sanders (I).

Rumor has it that final passage will come early on Wednesday.

Of course, as we discussed this morning, the Senate was always going to be the easier chamber on this agreement, and House Democratic leaders continue to demand changes. I’ve heard some fascinating rumors this afternoon on how the lower chamber intends to proceed, but before I could write anything up, Greg Sargent beat me to it.

Here’s the challenge for House Dem leaders right now, as I understand it: Come up with a way for Dem members to vent their disapproval of the deal, so they don’t feel too stiffarmed and marginalized by the process, without it resulting in changes significant enough to cause Republicans to walk away. The deal is expected to clear the House with a combination of strong GOP support and some backing among moderate Dems. Tweaking the bill in a way that drives away Republicans could imperil its survival.

The result could be a situation in which Dems hold a vote on amendments to the bill that are likely to fail. House Dems are particularly angry about the deal’s estate tax provision; Dem leaders could hold a vote amending that provision, allowing Dem members to register disapproval. But the amendment would likely be opposed by almost all Republicans and some moderate Dems. So it would likely lose.

I heard the exact same thing. The House could vote on the deal as-is, and at the same time, Dems who want to make their voices heard could save face — pushing principled amendments that reflect the kinds of changes they’d like to see, even if they’d come up short.

I also heard that as far as House Dems are concerned, they feel as if they’ve already delivered a message loud and clear to the White House — the party’s rank and file expect more hardball and fewer concessions from the president going forward. They feel as if their response over the last week, even if it comes up short on killing the agreement, has been ferocious enough to stick in the president’s memory for next time.

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Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.