As Senate negotiations continued on a plan to reopen the government and avoid default, it looked like the House would offer up a procedural present that could expedite a final resolution.

Senate Republicans scratched a scheduled 11 a.m. conference meeting, notifying senators that they would instead receive an update on the talks between Majority Leader Harry Reid, D-Nev., and Minority Leader Mitch McConnell, R-Ky., during the weekly conference lunch.

Reid offered very brief opening comments on the Senate floor Tuesday morning, saying “productive negations” with McConnell would continue.

Not much has changed in the big picture of the Senate package since late Monday, though one source familiar with the talks said that the proposal to delay implementation of a $63 per year reinsurance tax was out of the equation.

Another source wouldn’t verify that development but indicated that if Republicans succeeded in getting that Obamacare fee delay removed from the deal, a proposal regarding income verification for subsides and credits provided under the health care law would likely be out as well.

The House plans to move ahead with its own measure, including a delay in implementation of an excise tax on medical devices and a slimmed-down version of what’s come to be known as the Vitter amendment. The House version would hit lawmakers and members of the Cabinet but would not touch congressional staffers.

Neither of those pieces are on the table in the Senate negotiations, but the move is still good news for procedural reasons. Measures that have pingponged between the House and Senate in different forms are only subject to at most one debate-limiting cloture vote, even when the Senate offers an amendment (or even with just a simple majority, depending on the structure of the House offer).

In other words, Reid and McConnell could thank House Republicans for being able to avoid entering the uncharted procedural waters of the new expedited process for proceeding to legislation.

A House GOP aide said that the new House debt limit measure would be carried on the back of a continuing resolution that previously passed the House and Senate in different forms. That, of course, requires GOP leaders to actually pass their bill promptly, and it’s not yet clear they can do so.

Another item remaining for discussion as of Tuesday morning involved the ability of Treasury Secretary Jacob J. Lew to use “extraordinary measures” to forestall the final date by which the government exhausts borrowing authority.

Under the framework, that date would come on Feb. 7, 2014. The government would be reopened through Jan. 15, 2014. In addition, a House-Senate budget conference would need to report results by the middle of December.