President Barack Obama threatened on Friday to veto a House Republican bill that would keep government-backed student loan interest rates at their current level because of a poison-pill amendment, even though his veto would play directly into an obvious trap laid by Republican political strategist Karl Rove.

President Obama has said repeatedly that student loan rates must not go up — which they will on July 1 without Congressional action — and the Interest Rate Reduction Act would indeed accomplish those ends. However, it would do so by eliminating the Prevention and Public Health Fund, a key part of Obama’s health care reforms.

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“This is a politically-motivated proposal and not the serious response that the problem facing America’s college students deserves,” the administration said Friday in a policy statement (PDF), threatening a veto the bill if it lands on Obama’s desk.

The bill passed the Republican-controlled House of Representatives on Friday afternoon by a margin of 215-195, with votes falling mostly along party lines.

That veto could be issued at hazard to the president, who’s facing a political Catch-22 thanks to a new strategy hatched by former Bush political adviser Karl Rove. Rove’s political action committee, American Crossroads, has a new ad out this week that makes a pitch for the youth vote by condemning Obama as a “cool” president who’s somehow causing students to struggle.

The ad, which portrays Obama as a celebrity instead of a leader, focuses on growing student loan debt and other economic issues currently facing many American graduates. It asks at the end, “After 4 years of a celebrity president, is your life any better?”

If the president is forced to veto the booby-trapped student loan bill, it will enable Republicans to ultimately claim that the president is doing little to help young people. Without Congressional action, however, government-backed student loan rates will double on July 1, which will make college significantly more expensive for 7.5 million American students, according to the liberal think tank Center for American Progress.

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Pushing back against this likelihood, Obama issued a series of executive orders recently that allow graduate students to cap their loan repayments to 10 percent of their income, and forces the government to consolidate outstanding loans so students won’t have to repay multiple entities each month. His student loan push is what landed Obama on late night television recently with host Jimmy Fallon.

“This is something Michelle and I know about firsthand,” Obama told a crowd of students in North Carolina this week. “I just wanted everybody here to understand — I didn’t just read about this. I didn’t just get some talking points about this. I didn’t just get a policy briefing on this. Michelle and I, we’ve been in your shoes. Like I said, we didn’t come from wealthy families.”

The president’s chief political opponent, former Massachusetts Governor Mitt Romney (R), said in March that he would not promise any government help for students, and insisted that young Americans should not “expect the government to forgive the debt that you take on.”

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After sealing up his bid for the Republican presidential nomination, Romney completely reversed that position and embraced House Republicans’ booby-trapped student loan bill, telling reporters he fully supports it “because of the extraordinarily poor conditions in the job market.”

This video is from Karl Rove’s American Crossroads PAC, published to YouTube on April 26, 2012.

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[Photo: AFP / Win Mcnamee]

Updated from an original version to include the House vote count.