Updated 4:24 p.m. | House Republicans will attempt to re-amend a stopgap spending bill with a one-year delay of Obamacare’s individual mandate and a provision eliminating health benefits for members of Congress and their staff, Rep. Darrell Issa of California said today.

The move will be the House’s third attempt to get the Senate to agree to legislation that would undermine the president’s signature health care law. The House is expected to vote sometime tonight, but members cautioned it could be a late vote. The Senate voted earlier today to table, or kill, the House’s amendments designed to delay the entire Obamacare law for a year and repeal a medical device tax. Last week, the Senate voted to strip the House-passed continuing resolution of amendments that would defund implementation of the health care law.

After emerging from a 2 p.m. GOP Conference meeting, Rep. Bill Shuster, R-Pa., cautioned that the conference is not as united behind the newest plan as it was when leaders proposed on Saturday to delay the entire law for a year.

Shuster said members “overwhelmingly” support the newest plan, but he noted, “there are definitely some members who disagree with it.”

Former Republican Study Committee Chairman Jim Jordan, R-Ohio, for example, said he could support the plan — but just barely.

“Well, [it’s] keeping some of the harmful effects of Obamacare from being imposed on our constituents, so that’s a step in the right direction,” Jordan said. “And it’s respecting the rule of law, which is another important concept, obviously, with what it does for the member subsidy issue. And it keeps the government running.”

Asked how close Republican were to offering a plan that conservatives couldn’t support, Jordan said leadership was “real close.”

“This is reasonable, and if the Senate can’t take this, I don’t know what else there is to offer,” he said.

Rep. Tom Cole, R-Okla. — a close ally of Speaker John A. Boehner, R-Ohio — said he thinks “the conference is actually very united on this.”

He added, “It shows we’re not for Congress getting a special deal [on health care], and we’re not for the American people being stuck, you know, when everybody else is getting off, like big business.”

House Republicans also reiterated their contention that the Senate will be blamed for any government shutdown that occurs at midnight.

Rep. Michael C. Burgess, R-Texas, complained that the Senate was not compromising on the issue of Obamacare.

“It’s hard to negotiate with someone who doesn’t want to negotiate with you, and that’s the position we’re in right now.”

And he disputed the notion that Senate Majority Leader Harry Reid, D-Nev., had the advantage in the current shutdown showdown. Burgess noted that the Senate may be hard-pressed to vote against the amendment removing health benefits for members and their staff.

“I don’t think he’s got the advantages and again, we’ll send him some political kryptonite and see what he does with it,” Burgess said.