The bipartisan five-month unemployment insurance extension pending in the Senate appears to be driving a wedge between segments of the House Republican Conference.

Speaker John A. Boehner of Ohio and other House leaders portrayed the extension as unworkable after a three-month break in such benefits, and they are arguing for GOP alternatives to spur growth and job creation. But Rep. Peter T. King of New York said Thursday he and Rep. Frank A. LoBiondo of New Jersey had sent a letter urging Boehner and his team to move the Senate proposal (HR 3979) or an alternative.

“We want it extended,” King said. “We respectfully request that the House immediately consider this bill or a similar measure to restore unemployment benefits to struggling Americans,” the letter said.

The Senate voted, 61-35, to invoke cloture on the measure Thursday, clearing the way for passage Monday, leaving House Republicans to decide on how to deal with it.

Five Republicans besides King and LoBiondo signed the letter asking Boehner to bring something to the floor: Joe Heck of Nevada; Jon Runyan and Christopher H. Smith, both of New Jersey; and Chris Gibson and Michael G. Grimm, both of New York.

Rep. Cathy McMorris Rogers of Washington, head of the Republican Conference, said party leaders had not decided how to handle the measure and would discuss it next week. “There will be a conversation. We’re waiting to see what the Senate actually passes,” she said.

For some Republicans, the Senate measure presents an enticing vehicle for a flock of stalled proposals to cut taxes, curb regulations and undo mandates under the health care overhaul (PL 111-148, PL 111-152). If leadership decides to attach such provisions, they will have to weigh how far they believe they can go in pushing Democrats into a corner to accept the package before they invite criticism that they are obstructing the bill.

Rep. Steve Southerland II of Florida, a member of the leadership team, said the idea of adding GOP proposals had strong appeal. “I am always for doing things that get good policy done for us,” he said.

But he added that many conservatives favored allowing expiration of broader unemployment benefit that were created in 2008 in response to the financial crisis. “You have to overcome that argument. We need to do the right thing: allow the economy to create jobs,” Southerland said.

Democrats made clear Thursday they would press for quick House floor action on the Senate package, without changes. Majority Leader Harry Reid of Nevada said he had no plans to open talks with House Republicans to tweak the package.

“I want them to pass this,” he said. “They can do whatever they want. … Find out what they do, then I’ll react to it.”

Some Republicans have urged leaders to use the bill for action on a House-passed proposal (HR 803) by Virginia Foxx, R-N.C., to meld job training programs. The Foxx bill faces strong opposition from Senate Democrats including Labor, Health, Education and Pensions Chairman Tom Harkin of Iowa, who has advanced a separate job training plan (S 1356).

Rep. Charlie Dent of Pennsylvania, a leader of the centrist Tuesday Group of Republicans, said he was urging party leaders to combine the Senate measure with at least one of a trio GOP priorities. They include medical device tax repeal, approval of the Keystone XL pipeline and an increase (HR 2575) in the work-week trigger for the employer mandate to cover full-time employees under the health care overhaul. “I offered three suggestions. If I got one, I’d be happy,” Dent said.

Sen. Barbara Boxer, D-Calif., said she doubted any of them would be acceptable as add-ons to the measure.

Sen. Jack Reed of Rhode Island, the Democrats’ point person on jobless aid, said any negotiations likely will be handled in the House. Assistant Minority Leader James E. Clyburn of South Carolina said Democrats were not planning to open talks on any changes, for now, and instead would press House leaders to allow a floor vote on the Senate package.