President Obama won goodwill on Capitol Hill by successfully killing Osama bin Laden, but not enough to overcome Republican demands on the debt limit, a GOP lawmaker said Tuesday.

Rep. Cynthia Lummis (R-Wyo.), a second-term lawmaker, said that the political capital Obama accumulated by launching the successful mission to assassinate bin Laden wouldn't tick the needle in the spending fight with Congress.

"It does create goodwill in Congress and around Washington," Lummis said of bin Laden's death during an appearance on the Fox Business Network. "I don't believe that translates to a change in philosophy when it comes to the debt ceiling."

Obama is seen as likely to enjoy a bump in his approval ratings, at least in the short term, due to the bin Laden killing on Sunday. That could mean the president feels more emboldened to stare down House Republicans over an impending fight over raising the debt ceiling, and what kind of accompanying spending cuts and reforms are attached to that vote.

Lummis said she expected the bin Laden news to affect the politics, but she expressed confidence in House Speaker John Boehner (R-Ohio) to stand strong on the issue.

"It will translate into the politics of debt reduction, but I believe John Boehner's hand is equally strong," she said.

"We're still going to have our differences," Lummis explained. "The president seems still to want a clean increase to the debt ceiling. I believe most members of Congress want assurance that we're addressing our long-term structural problems going forward, along with the debt ceiling."

Updated at 12:55 p.m.