One House bill, backed mostly by Republicans, would repeal a tax imposed on some medical devices to help pay for former President Barack Obama's health care law, a statute they despise. With another, still a bare-bones outline, the GOP would make last year's $1.5 trillion tax cut permanent and expand reductions for families, homeschooling, and businesses.

House Democrats have a plan for helping students afford the growing costs of college, in part by creating a partnership with states to provide two years of tuition-free community college. It would also expand the size of Pell Grants, which largely go to undergraduates from lower-earning families.

Lawmakers promoted each of these proposals Tuesday, though none seems likely to become law soon. But they typify a time-sensitive priority for both parties: honing their messages for elections, just over 100 days away, in which congressional control is the prize.

The House starts summer recess at week's end, and lawmakers need arguments to take home for town halls and campaign advertising and to rev up voters and contributors. Democrats need to gain 23 seats in November's midterms to capture House control, which is widely seen as doable, so both parties are producing bills to shore up political weak spots or play offense.

For House Speaker Paul Ryan, who is retiring, that meant giving Republicans credit for the strengthening economy and using Democrats as a foil, perhaps offering a GOP playbook for fall campaigns.

"They've scoffed at Americans who've benefited from more money in their paychecks," he told reporters, a reference to House minority leader Nancy Pelosi's comparison of GOP tax cuts for the wealthy to the "crumbs" that went to lower earners. "They're determined to erase this progress. Even more, they want to take this country to a dramatically different place, to the far left."

As evidence, Speaker Ryan cited recent proposals from Democrats' liberal wing to abolish United States Customs and Immigration Enforcement and push for "Medicare for All," or government-paid health care. Many Democrats have distanced themselves from both ideas.

Democrats happily returned the favor. They announced their "Aim Higher Act," which would make higher education more affordable and restrict federal aid for for-profit schools often criticized for huge student loan defaults. They contrasted it with a GOP bill that would create new partnerships between colleges and industry but also limit how much federal education money students could borrow.

"We want a world where parents don't have to choose between college for their kids or paying the rent," said Rep. Susan Davis (D) of California.

A critical challenge facing GOP messaging plans is Mr. Trump, who dominates the political stage by abruptly swerving onto issues that put Republicans on the defensive. In recent days, that's included extolling Russian President Vladimir Putin while challenging his own intelligence and law enforcement agencies, defending tariffs he's imposed that threaten trade wars and considering the removal of security clearances for political opponents. He's since said he trusts US intelligence, but he also invited Mr. Putin to the White House.

With their latest tax cut push, Republicans hope to draw attention to an age-old GOP priority and appeal to key constituencies, including businesses, high-earners, and conservative homeschooling families.

Republicans are paying particular attention to health care, which polls show remains a major concern to voters. Democrats see it as their issue, thanks to lingering resentment over GOP efforts to dismantle Mr. Obama's now-popular law. With most states planning to unveil 2019 premiums just before the elections and many expecting significant increases, Republicans who have dominated Washington since January 2017 say they need to show progress, or at least blame Democrats for lack of it.

"Moderates and independents, that group right now is not in love with Republicans," said Rep. Barry Loudermilk (R) of Georgia. He said Republicans must show those voters that "we're trying to head in the right direction" but are being blocked by Democrats.

Addressing that concern, Republicans pushed a bill through the House on Tuesday eliminating the 2.3 percent tax on many medical devices. The measure seems unlikely to survive in the Senate, where Democrats have enough votes to derail it.

The tax doesn't apply to devices like eyeglasses or hearing aids but does hit items used or provided by professionals, including X-ray equipment and hip implants. It's estimated to raise less than $20 billion over the coming decade – a tiny portion of the health care law's costs. Republicans call it a job killer, which Democrats and some outside analysts say is overblown.

Also moving in the House this week are a GOP bill helping people buy health insurance with skimpier coverage than Obama's law allows and a measure letting people use tax-advantaged health savings accounts to buy over-the-counter drugs.

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In the Senate, which is planning a shorter recess, the brewing fight over Supreme Court nominee Brett Kavanaugh is becoming another messaging battlefield. Republicans are using Mr. Kavanaugh's record on issues like gun rights and religious liberty to energize conservative voters, while Democrats are reaching out to their supporters by citing their expectation that he would rule against abortion rights and Obama's health law.

This story was reported by The Associated Press.