Forty-three House Republicans have introduced their own continuing resolution that they think would achieve the goal of both cutting spending and defunding Obamacare better than the plan GOP leaders put forth Tuesday.

Rather than fund the government for a month and a half at the post-sequester top line of $988 billion, it would run through all of fiscal 2014 at the lower, $967 billion levels many Republicans favor.

And, instead of relying on a legislative maneuver to force the Senate to vote on defunding Obamacare without risking a shutdown at the end of the month, it contains language that would actually zero out funding for the president’s signature health care law.

It could spell trouble for the Ohio Republican and other members of the leadership team as they try to come up with a strategy that won’t alienate their base but has an actual chance of passing the Senate.

“Our plan will achieve fairness for every American by fully delaying and defunding Obamacare until 2015,” Rep. Tom Graves of Georgia said in a statement. “This approach builds upon the Obama Administration’s policy of delaying portions of Obamacare and relieves taxpayers of the burden of funding a program that is not being implemented.”

Heritage Action for America likes the sound of this.

“Rep. Graves and his colleagues are stepping up to fill a critical void in the House,” said Mike Needham, the group’s CEO. “We encourage all members to support the Graves bill.”

Though this might have the votes to pass the Republican-controlled House, the chance for getting the green light from the Senate and the White House appears even less likely than the plan GOP leaders presented to members earlier this week.

“As we all know, the speaker has a problem, how to get the government funded,” Senate Majority Leader Harry Reid, D-Nev., said Thursday. “I told him very directly that all these things they’re trying to do on the Obamacare is just a waste of their time.”

Here’s a full list of the 42 current GOP co-sponsors of the new, Graves-led CR proposal, some of whom — such as Rep. Trent Franks of Arizona — told CQ Roll Call earlier this week that they were inclined to support the initial leadership strategy should that ultimately come to the floor for a vote.

Jim Jordan of Ohio

Mark Meadows of North Carolina

Jeff Duncan of South Carolina

Steve Southerland II of Florida

Doug Collins of Georgia

Raúl R. Labrador of Idaho

Trey Gowdy of South Carolina

Randy Weber of Texas

Pete Olson of Texas

Tom Marino of Pennsylvania

Steven M. Palazzo of Mississippi

Joe Pitts of Pennsylvania

Paul Broun of Georgia

Matt Salmon of Arizona

Jim Sensenbrenner of Wisconsin

Richard Hudson of North Carolina

Jeb Hensarling of Texas

Ron DeSantis of Florida

Lynn Westmoreland of Georgia

Thomas Massie of Kentucky

Phil Gingrey of Georgia

Jim Bridenstine of Oklahoma

Mo Brooks of Alabama

Bill Cassidy of Louisiana

Randy Neugebauer of Texas

David Schweikert of Arizona

Scott Perry of Pennsylvania

Blake Farenthold of Texas

Bill Huizenga of Michigan

Luke Messer of Indiana

Bill Flores of Texas

Mick Mulvaney of South Carolina

Tim Huelskamp of Kansas

Steve Daines of Montana

Joe Wilson of South Carolina

Marsha Blackburn of Tennessee

Reid Ribble of Wisconsin

Tom Price of Georgia

Austin Scott of Georgia

Marlin Stutzman of Indiana

Trent Franks of Arizona

Steve Chabot of Ohio