House Rules Chairman Pete Sessions of Texas and other senior Republicans are pushing proposals to tie the extension of emergency unemployment insurance to jobs measures and the extension of some tax breaks in an attempt to bring the plan to the House floor.

Majority Whip Kevin McCarthy of California said Tuesday there was no plan to deal this week with the five-month unemployment extension (HR 3979) that passed the Senate on Monday and that any potential action on a House GOP alternative likely would come after the two-week April recess.

“I don’t think the Senate bill is one that can pass the House,” McCarthy said.

The comments from senior Republicans were the strongest indication from GOP leadership, however, that the House may take up some form of an unemployment extension.

Sessions said the five-month extension could serve as a partner for House-passed bills and other priorities, such as a permanent extension of so-called bonus depreciation for business investment.

“I’m engaged in conversation with others about putting accelerated depreciation on,” Sessions said.

Senate Majority Leader Harry Reid of Nevada said he was pleased to hear the suggestion that Republicans may “attach some jobs bills” to the jobless aid extension. “So, I’m sure we’ve made some progress,” Reid said.

Sessions said House Republicans would weigh options in coming days, and likely pursue informal talks with senators in the meantime.

“It will depend how reasonable both sides are. We see what their offer is. I think that we could offer back an equally reasonable circumstance,” Sessions said.

“The president and Democrats have refused to allow jobs bills. They are stacked up in the Senate. They want what they want. Well, the American people need a chance for a job,” he said.

“We would like to see a very robust plan to have economic growth,” McCarthy said.

Sessions’ suggestion that expired temporary tax breaks could be included in the jobless package was the first time the so-called extenders have arisen in the debate between the House and Senate over the unemployment aid that expired Dec. 28.

But including any tax provisions may short-circuit a plan by Ways and Means Chairman Dave Camp, R-Mich., to mark up separate tax cut extension measures later this year. Camp said he had no plans to bundle them with jobless aid.

“It’s not something the committee is considering,” he said.

Other members of his panel said linking of tax cut extensions to jobless aid could attract consensus support, however.

Rep. Peter Roskam, R-Ill., chief deputy whip and a senior tax writer, said no decision had been reached on add-ons, but that some lawmakers were floating ideas. “There’s a lot of discussion of merging UI to this or to that, energy and other things,” Roskam said.

Rep. Dave Reichert, R-Wash., another tax writer, the jobless aid package could be a vehicle for measures aimed at helped the unemployed get work, as well as extensions of expiring tax breaks.

Rep. Kevin Brady of Texas, another senior tax writer, said adding just one popular extended tax break like bonus depreciation would not sway him.

“Nothing in my view, short of a jobs bill, a real significant jobs bill, would convince me to vote for that. I really want a much stronger economy. I don’t think any single tax provision can achieve that,” Brady said.

Democrats held a rally Tuesday to urge House Republicans to take up the Senate package. Supporters pointed to a Congressional Budget Office study that showed that a full-year jobless aid extension would add 0.2 points to economic growth. The shorter duration of the Senate proposal means “the benefit to the economy will likewise be smaller,” Seth Carpenter, a Treasury assistant secretary, wrote in a blog post on Tuesday.