Last year, candidate Donald Trump promised to repeal Obamacare and give Americans a better, cheaper replacement. Last month, President-elect Trump vowed, "we'll be filing a plan" as soon as the Senate confirmed his Health secretary.

But, post-confirmation, Health Secretary Tom Price has told House Republicans "the administration wouldn't be sending us a bill" after all, said Rep. Tom Cole of Oklahoma. Instead, Cole added, the White House "will cooperate and provide input into what we do."

Two weeks ago, Trump said at the White House that "we're going to be announcing something over the next, I would say, two or three weeks that will be phenomenal in terms of tax." But House Republicans do not expect the president to announce his own tax plan; instead, they anticipate he will simply align himself with theirs.

A more hands-off approach than Trump has previously signaled doesn't mean that the Republican agenda won't succeed; in 2009, President Barack Obama let congressional Democrats fill in the details of what became Affordable Care Act. But it heightens the political risks, both for the agenda and for individual Republican members looking anxiously toward 2018 midterm elections.

For the agenda, the risk is that the absence of White House plans may complicate prospects for achieving consensus between the more ideologically aggressive House and a more centrist Senate. For individual Republican members, the risk is that a president of their party may turn against controversial elements of tax or health plans after they've voted for them.

For now, lawmakers and congressional aides say the White House has worked closely with them as they craft their own approaches. When it's "go time" for legislation, as one House leadership aide put, Republicans are counting on Trump to provide the strong public advocacy needed to overcome political resistance.

The House is much further along than the Senate. On health care, House Republicans aim to repeal Obamacare and replace it by Easter with a system of tax credits, health savings accounts, "high-risk pools" for the sickest Americans and a plan to cut Medicaid spending using per capita limits on beneficiaries.

On taxes, they have an equally ambitious objective: enactment by August of a comprehensive overhaul of individual and corporate taxation. Their plan would cut the top individual income tax rate to 33 percent from 39.6 percent and cut the top corporate rate to 20 percent from 35 percent, financed in large part by a new border adjustment tax hitting imports and exempting exports.

While the Senate struggles to formulate its approaches, House Republicans say they communicate constantly with the White House. The long-standing friendship between Speaker Paul Ryan and chief of staff Reince Priebus helps smooth their relations.

But they haven't achieved consensus, yet. While chief White House strategist Steve Bannon strongly backs the House border adjustment tax plan, National Economic Council Director Gary Cohn has reservations. So do some Republican senators, leaving its prospects in doubt.

At the same time, Treasury Secretary Steven Mnuchin has said publicly that Trump-era tax reform will provide no net tax cut to the most affluent taxpayers; any benefit from rate cuts, he explained, will be offset by lost deductions. In fact, the House Republican tax plan provides a large tax cut for top earners, and Ryan has specifically rejected squeamishness over that fact as the sort of thing that offends Democrats, not Republicans.

For all their optimism over unified Republican control of Congress and the White House, lawmakers acknowledge they face immense political difficulty on both tax reform and health care. They cannot succeed without Trump, but the help he intends to provide will not be enough to amass House and Senate majorities.

"It really is up to us," Cole said, "to get that done on our own."