House Majority Leader Eric Cantor and his staff are working behind the scenes to avoid another embarrassment this month when they bring to the floor a bill that would increase funding for pediatric research.

The measure is part of the Virginia Republican’s agenda to soften the Republican image. But it is running up against the same hardline conservatives who forced leaders in April to pull from the House floor a bill (HR 1549) that would have reprioritized funding within President Barack Obama’s health care law (PL 111-148, PL 111-152).

The ideological divide within the party is apparent in these two bills. While Cantor wants to use existing government funds to finance causes the GOP could support, some conservatives would just as soon see that money not spent at all.

“Legislating, especially in times of fiscal stress, is about prioritizing,” Cantor said Thursday on the House floor. “I’m very much in favor of making a priority out of federal research and development. … But it doesn’t mean necessarily that because we are going to commit ourselves to balancing the budget that we cannot share that priority.”

The latest wrinkle comes with the Kids First Research Act (HR 2019), which would end taxpayer funding of presidential campaigns and party conventions and divert that money instead to the National Institutes of Health to fund pediatric research.

Conservatives would rather see the funding eliminated outright. In a May blog post on the Heritage Foundation website, Hans von Spakovsky and Emily Goff of the conservative think tank wrote that, “while ending this public election financing program is a good idea, turning around and authorizing funding for another program wipes out that progress and sets up a whole new constituency for government spending.”

It’s unclear whether Heritage Action and other conservative advocacy groups would go so far as to make the measure a key vote, but the opposition from such groups is likely to draw at least some House conservatives into the “no” column. As a result, Cantor and the bill’s GOP co-sponsors, Reps. Gregg Harper of Mississippi and Tom Cole of Oklahoma, are reaching out to Democrats for support. They even removed a section from the first version of the bill (HR 1724) that would have made it harder for the NIH to research health economics in order to please Democrats who favor the research, according to a Republican aide.

“Cantor’s obviously trying really hard to not just be about deficit reduction while also trying to reduce the deficit,” a senior GOP aide said. “It’s hard, when for four years many of these issues have been on the back burner as we focused on controlling the size of government spending, you start talking about all these things and it takes time.”

The bill is expected to come to the floor either this week or next, and it may even come under suspension of the rules, which makes it easier to bypass committee consideration. That would avoid some public scrutiny from conservatives, but it also would require a two-thirds majority vote for passage.

“It is a high hurdle, but it really would be the right thing to do and I’m hopeful,” said Harper. “I do think that when this is explained and looked at by anybody, regardless of their philosophical leaning, they’ll say this is one that ought to get through.”

But conservatives are skeptical that the move is just a ploy to skirt around their opposition and also pin the bill’s possible failure on Democrats. Although leadership aides said they will not bring the bill to the floor unless they are certain it will pass, other GOP sources speculated that they could craft effective campaign advertisements against Democrats who vote against boosting research funds.

Democrats do not necessarily agree with defunding the public presidential campaign fund. When Harper brought to the floor a bill last Congress that repealed the fund and used the savings to reduce the deficit, no Democrat voted in favor and only one Republican, Rep. Walter B. Jones of North Carolina, voted against.

In this effort, though, six Democrats have signed up as co-sponsors because of the boost in NIH funding, including Rep. Peter Welch of Vermont, a chief deputy minority whip who is trying to round up support in his caucus.