Aides to Mr. Ryan, who in a speech last year called for “a complete alternative to the left’s agenda,” say the effort will be clearer after this week, when the House is expected to vote on a measure to defund Planned Parenthood and repeal part of the Affordable Care Act. The measure, which already passed the Senate as part of a procedure known as reconciliation, is expected to be vetoed by President Barack Obama. But it will allow Republicans to dispense with two topics that are big priorities for conservatives, then shift to a broader agenda.

While Mr. Ryan is soliciting ideas from the rank and file, he has made clear he believes the party should tackle an overhaul of the tax code, which could include consolidating tax brackets and lowering rates but also targeting some popular tax breaks. He has also promised that the party come up will this year with a health-coverage plan that would replace the Affordable Care Act.

Mr. Ryan isn’t unique in trying to use the chamber to help guide a party’s agenda in an election year.