With votes scheduled on a series of coveted trade deals this week, one would think House Majority Leader Eric Cantor (R-Va.) would stack the deck with noncontroversial votes to provide his Conference with a week’s worth of jobs-related wins.

After all, Republicans have struggled for much of the year to break through the constant string of emergency spending and debt measures with their jobs agenda, and public polling shows voters trust an unpopular President Barack Obama with the economy more than they do Congressional Republicans.

And yet Cantor has decided to use Thursday for a floor vote on a bill to prevent federal funding for health care plans that provide abortion services — a topic guaranteed to polarize.

Although part of the reasoning behind taking the vote this week was that the trade wins could give the House some cover to pass the bill without fanfare, Republicans acknowledge the chance that the vote could muddy an otherwise solid week for the GOP’s jobs message.

“Why are we doing this?” one veteran GOP aide asked.

“I don’t think anybody believes that’s going to bring jobs, nor does anybody believe that’s going to pass,” Minority Whip Steny Hoyer said Tuesday.

“It is taking time up for political agenda, which has little chance of doing anything other than appealing to those people who believe it’s an appropriate policy,” the Maryland Democrat added.

On Friday, Cantor announced that the House would be taking up abortion this week. In a speech before the conservative Values Voter Summit in Washington, D.C., Cantor said, “[This] week we will stand up again” to pass legislation so that “no health care worker has to participate in abortions against their will.”

Cantor also went after Planned Parenthood in his speech, telling the gathering of activists, “I can tell you that after November 2012, we look forward to a Senate and a White House that will partner with us” to kill funding for “any and all organizations that perform abortions.”

But during his weekly meeting with reporters, Cantor was back on the GOP’s jobs agenda, the Joint Committee on Deficit Reduction and even the Occupy Wall Street protests. Absent from his prepared remarks was anything about the abortion vote.

Although abortion has not been a major part of the GOP’s internal agenda for the fall, Cantor’s office had informed lawmakers earlier in the week that the bill would come to the floor, several aides said.

The decision to take the vote also comes despite public and private demands by top Republicans that jobs and the economy become the primary focus of the GOP this fall as well as admonishments to conservatives that the House must abandon the ugly partisan fights that have marred the 112th Congress.

In September, for instance, Cantor said Republicans would “focus like a laser on growth,” and on Tuesday during his weekly meeting with reporters, the Virginian argued that the Senate and Obama administration should drop their demands for stimulus measures that are politically untenable.

“Stop putting stuff forward that doesn’t have the bipartisan support necessary” for passage, Cantor said. At one point, the GOP leader pointed to Senate jobs legislation that Republicans say spends too much and ruled it dead on arrival in the House. “It just doesn’t make sense to us, and we’re not going to pass that,” Cantor declared.

But when asked how he squares demands for bipartisanship by Democrats with his plan to pass an abortion measure with no chance of passage in the Senate, Cantor said simply, “That was part of the Pledge to America. … It is something we said we would do, and we’re upholding that pledge.”

GOP aides defended Cantor’s decision, noting that the Pledge to America locked Republicans into a number of votes on abortion and that if he didn’t stick to it, Republicans would “get hit with a bunch of bad stories.”

Cantor is also dealing with a particularly motivated part of his caucus. Rep. Joe Pitts (R-Pa.) — who sponsored the bill — is one of the House’s most virulently anti-abortion lawmakers and enjoys support from a significant portion of the GOP Conference.

As a result, even if Cantor and other leaders did not want to take up the issue again, they would have likely had little choice but to address it in some way.

A leadership aide also dismissed questions about the timing of the bill, saying that regardless of when Cantor brought it to the floor, it would be a contentious vote.

“When would you like us to have the vote?” the aide asked.

Still, Hoyer questioned the logic of bringing up a bill that has little chance of passage.

“There’s not a Republican who believes that bill is going to be passed in the Senate — I think, maybe I’m wrong on that — or that the president would sign it,” he said Tuesday.

Jessica Brady contributed to this report.