From a NYT editorial yesterday, “No Crime, No Punishment”, p. 10:
Proving federal fraud requires evidence of intent, no small lift.
Or framed positively, a big lift ‘something which is a lot to lift (i.e. achieve)’. Not among the many senses of the deverbal noun lift in the OED, but similar to a big ask ’something which is a lot to ask’ as discussed on Language Log back in 2008.
The nouning lift has been around in English since the 15th century, according to OED2, originally in the sense
The action or an act of lifting, in various senses of the vb.; a raising or rising; the distance through which anything is lifted and moved.
Other senses quickly proliferated, for example:
In various immaterial applications, e.g.: A ‘rise’ in station, prosperity, etc.; promotion; a rise in price; an act of helping, or a circumstance that helps, to a higher or more advanced position. [from 1622 on]
A help on the way given to a foot passenger by allowing him to travel some distance in a vehicle. [from 1712 on]
An elevating influence or effect. Also, a cheering or encouraging influence or effect, a sense of elation. [from 1825 on]
Googling for “a big lift” in the sense ‘something which is hard to achieve’ is very difficult, since the ‘elevating influence’ sense is so very frequent. But a hard lift in this sense is easier to find; for instance:
Russia trade vote will be “hard lift”: U.S. lawmaker [Rep. Kevin Brady] (link)
It was a hard lift whipping the votes in the House to pass the thing [the 2003 Medicare reform bill] since many conservatives objected, but they got it done. (link)
Most of the hits for a hard lift are, however, for lift in still another sense; from the OED draft additions of 1997:
Sport. Any of the set movements by which a weight-lifter lifts a weight or a wrestler lifts an opponent. [cites from 1908 on]
How much rest does a muscle group need after a hard lift? (link)
A hard lift ‘something that is hard to achieve’ might well have originated from the weight-lifting usage.
A big lift, no small lift, etc. in that sense might then have developed from such uses of a hard lift, or by analogy with a big ask ‘something which is a lot to ask’, or simply by analogy to a big task / undertaking / endeavor / achievement / accomplishment (that is, as a fresh nouning of the verb lift). Or all of the above. It’s probably been around for a while.