Schumer and McConnell reached an agreement to delay the trial itself until the 8th (i.e. next week), partly to give Trump's team time to figure out a defense, and partly to give the Senate time to confirm more cabinet positions before getting stuck in the trial for a while.
As to the $2k thing, is the objection about the amount of money or the timing?
For the former, the $2k was a discussion before the $600 agreement was reached so I don't think it's completely out there to be talking the additional $1400 now. (That said, I do think once the December bill was reached they should have changed their talking points / framing.)
For the latter, they really doing it pretty much as fast as they can - remember that the Senate didn't technically flip until the 21st of January, crafting the reconciliation format needed to do filibuster-free votes requires jumping through hoops that takes some time, and that they don't have the votes to nuke the filibuster. At this point it'll likely be another several weeks (late February or March) before they can get the reconciliation bill fully passed. Reconciliation is an awkward process.
(Though yes, they were a mixture of naive, lying, and/or 'truthinessing' to say it'd happen immediately. It could if there was R support, but that's a pipe dream.)