House Republicans are honing their jobs message — crafting hard-to-oppose, small-bore bills, shipping them to the Senate and daring Democrats and the White House to take up the mantle of obstructionism.

The strategy paid off last week, with the White House signing on to a Republican bill eliminating a 3 percent tax withholding requirement for government contractors — a rare bill that appears likely to zoom to the president’s desk.

The quick White House acquiescence came as a bit of a surprise to House and Senate Democrats, some of whom fear the president’s $447 billion jobs package will be sliced and diced to the GOP’s liking with Democratic priorities left on the cutting-room floor.

But unlike many past efforts by both parties this year, the withholding bill appeared devised to become law, marrying a piece of President Barack Obama’s jobs package with a piece of his deficit reduction plan.

Legislating, instead of passing messaging bills or holding show votes, could be the new path forward, at least for now. That’s assuming House leaders can draft more pieces like the withholding bill and string together some victories.

“That’s the question: Are there a lot of other things like this?” asked Rep. John Campbell (R-Calif.). “There’s no question there’s a hunger to do things that get all the way to the finish line.”

Republican leaders have ramped up calls on the Senate to take up the “Forgotten 15” bills they have already passed that they say would create jobs, but few of those have much of a shot at becoming law.

Still, they used the list and the success on the withholding bill — it passed 405-16 — to parry the White House rollout of its “We Can’t Wait” message that blasts the GOP for blocking the larger jobs package and offers up a host of administrative actions aimed at producing jobs without Congress.

House Republicans are hoping for a similar result this week.

“If the president wants to do something meaningful to create jobs, he can start by working with Republicans and actually engaging in the legislative process,” said Brendan Buck, spokesman for Speaker John Boehner (R-Ohio). “But we can’t wait for him, so Republicans are going to pass and send to the Democrat-run Senate two more job-creating bills aimed at helping small businesses expand and hire.”

The two bills would reduce regulations for some small businesses and make it easier to access credit, Republicans said — items Obama mentioned in his jobs speech.

Republicans said they’ve been open to working with the president for months now.

“So now we’re doing what we can to prove there’s common ground in an attempt to convince the president to stop campaigning and to work with us,” a senior GOP aide said.

Democratic leadership aides said the withholding bill is likely to sail through the Senate this week — but that it won’t help the GOP. Republicans, they said, have changed their tone after the bruising debt ceiling debate but haven’t fundamentally changed their approach.

“It’s still brinkmanship and obstructionism, but with a nicer face on it,” one leadership aide said.

The larger perception that the GOP is blocking the president’s jobs bill won’t change, they said, if a few narrow provisions become law.

Small-ball ploys have no chance of penetrating the Beltway bubble, they said, and they point to Congressional Republicans’ poor poll numbers as evidence. Some 71 percent in a CBS/New York Times poll last week said Congressional Republicans don’t have a clear jobs plan.

Senate Democrats, meanwhile, are expected to push ahead with their plan to hold a vote this week on an infrastructure package taken from the president’s jobs package. It will be tied to a millionaire surtax the GOP has already rejected several times and is sure to do so again.

Don Stewart, spokesman for Senate Minority Leader Mitch McConnell (R-Ky.), said Senate Democrats need to decide whether they want to legislate or just go along with their plans to try to whack the GOP.

“Do they want to actually pass legislation that will help create a better environment for jobs — or do they just want to continue their strategy of proposing legislation that’s designed for failure and 30-second ads?” he asked.

Republicans have repeatedly charged Democrats with trying to dismiss the GOP’s efforts to work with them — including the passage of a patent reform bill and free-trade agreements — arguing they need to paint the GOP as the bogeyman, given the state of the economy.

McConnell noted last week on CNN that Obama declined to hold a big bipartisan signing ceremony for the trade agreements.

“They’re ashamed to … mention any of the things that they do with Republicans because it steps on their storyline. Their storyline is that there must be some villain out there who’s keeping this administration from succeeding.”

White House Press Secretary Jay Carney, meanwhile, kept up the drumbeat Friday that Republicans are blocking items that even GOP voters support.

“Republicans out in the country support building roads and bridges and schools. They support putting police officers and teachers back to work. They support tax cuts for everyone who receives a paycheck,” he said.

The fate of that larger $447 billion jobs package, meanwhile, is likely tied to that of the super committee tasked with coming up with a deficit reduction package. Democrats have already proposed adding several hundred billion dollars in stimulus measures to any package, which would be a major carrot to get Democratic votes for what might include difficult cuts in Medicare and other programs supported by Democrats.