On day five of the government shutdown and Congress’s second consecutive Saturday session, House Democrats made more overtures to Republicans in an effort to keep the pressure on them and show the outside world that they are willing to negotiate.

Whether the GOP is prepared to bite, or whether Democrats are making the kind of concessions necessary to satisfy a small group of centrist Republicans who want very specific sweeteners as conditions of voting to reopen the government or raise the debt limit, remain to be seen.

Democrats announced Saturday that, in exchange for Republicans appointing conferees to hash out a long dormant budget resolution, they would forfeit their right to offer a “motion to instruct” the House conferees. That’s a tactic minority lawmakers are allowed to employ if a conference report hasn’t been filed within 20 days of appointing conferees. It’s also one of the few devices available to the minority party to break majority hegemony in the House.

A motion to instruct, while non-binding, would essentially tell conferees to take a certain position in the House-Senate conference negotiations. It’s often designed to put members on record on a politically loaded position.

Speaker John A. Boehner, R-Ohio, said last April that he was reluctant to appoint conferees because motions to instruct “become politically motivated bombs to throw up on the House floor.”

“We will give up that right,” said the Budget Committee’s ranking member, Chris Van Hollen, D-Md., on Saturday.

A conference on the budget would be a victory for House and Senate Democrats, who have been clamoring for the opportunity to negotiate with Republicans on a comprehensive spending blueprint before passing individual spending bills in their respective chambers.

The timing of finally convening a bicameral budget conference would also be significant given the current Oct. 17 deadline for Congress to agree on legislation to raise the debt limit. It’s becoming likely that the debt limit will be rolled into a package that also contains a government-funding continuing resolution along with some provisions on deficit reduction.

Minority Leader Nancy Pelosi, D-Calif., said she made Boehner aware on Saturday morning that Democrats were prepared to take the threat of a motion to instruct off the table if Republicans would go forward with appointing budget conferees. She said Boehner “knows it’s a good faith effort on our front.”

But the speaker remained unmoved.

“At this point, it’s Senate Democrats and the President who are blocking progress on reopening the government and providing the American people fairness under ObamaCare,” said Boehner spokesman Michael Steel in an email to CQ Roll Call.

Doug Heye, a spokesman for Majority Leader Eric Cantor, R-Va., was similarly oblique on what Republican leadership thinks of Pelosi’s offer: “What Washington needs to do is come together and talk so we can re-open our government, and that is exactly the House Republicans’ focus.”

Almost 20 House Republicans have said they would support a “clean” CR, and they have expressed interest in creating a more hospitable environment for spending negotiations between the two parties. On Saturday, Democrats made sure to let those Republicans know they won’t be let off the hook for not engaging in the minority party’s efforts.

“We are holding [them] accountable,” said Steve Israel of New York, chairman of the Democratic Congressional Campaign Committee. “You cannot act like an independent pit bull at home and act like a tea party lapdog in Washington.”

Earlier this week, Democrats began to circulate for signatures a letter calling on Boehner to bring a “clean,” short-term continuing resolution to the floor. They announced Saturday that they had garnered 200 Democratic signatures (195 excluding five non-voting delegates). No Republicans have signed on so far.

On Friday, Democrats offered a “discharge petition” to force a vote on a clean CR, which Republicans are also generally disinclined to support.

Currently, the only proposal which House Republicans will support on the record is one being spearheaded by leading GOP moderate Rep. Charlie Dent of Pennsylvania and New Democrat Coalition Chairman Ron Kind of Wisconsin. That proposal calls for a six-month CR at sequester levels and a repeal of the medical device tax that funds parts of the health law. Dent said on Saturday that about 20 of his GOP colleagues were on board.

Democratic leadership isn’t excited about the idea, though, with Pelosi saying last week that she didn’t like a CR that maintained the sequester number for an extended length of time. Van Hollen reiterated that negotiations about issues such as taxes belong in the context of the budget, not a continuing resolution.

A handful of Republicans said Saturday that one impediment to moving this proposal forward lay in pressure from senior Democrats to members of their caucus not to endorse any solution to the fiscal impasse unless it involves a clean spending bill.

A Democratic leadership aide denied that any formal deterrents were taking place on the Dent-Kind initiative, and added that it made sense that it was the only proposal so far that would garner on-the-record support from significant number of Republicans.

“Of course Republicans like it best,” the aide said. “It repeals the medical device tax and it would hold their number longer.”