The Budget Act provided for "deeming resolutions" which means that if one chamber passes the budget resolution, but the other does not, the resolution is "deemed" passed for the purpose of placing mandatory spending targets on each appropriations subcommittee and the Appropriations Committee of that chamber. This does not solve the problem of the other chamber working with a different (internal) set of targets or with targets different from the Administrations budget. The 2010 article refers to an extra twist added to one such "deeming resolution" which was what to do about the ACA. The "payfor" to fund the ACA was very controversial. In effect, some revenue items started immediately and others started on 1/1/13, even though the real health care plan would not kick in until 2014. So if the ACA were repealled totally and immediately before 2014, the Republicans would be giving up the revenue sources that represented the downpayment on future health benefits. This would make the deficit larger than the baseline deficit forecast. Ryan's proposal was to say that ACA repeal would not count for the purposes of the "deeming" resolution and budget measurement if Ryan said it should not.
A historic precedent of similar activity was the Gephardt Rule which was in effect from 1979 to 1995. Under the rule, when the House approved a budget with spending greater than forecasted revenue, the House was "deemed" to agree to raise the debt ceiling by the amount necessary to cover the difference, and then the Senate had to vote to accept that increase (leaving the Senate with dirty hands, but the House members' voting records clean on the debt ceiling issue.) The point is, cute procedural rules can set up, but that is just for finger pointing rather than taking responsibility to make tough spending decisions.