To counter Democratic arguments that the GOP is out of touch with today's harsh economic realities, Republicans say the priority should be finding ways to create jobs, not erase them, such as by reducing taxes on companies.
"You can try to wave a magic wand and artificially" increase wages, said Republican pollster David Winston. Instead, he said, the GOP is reaching out to voters "who'd like to be earning more money and really think the economy needs to be turned around."
Key constituencies oppose compromising on a lower figure, including the AFL-CIO, which backs an increase, and the National Federation of Independent Business, which opposes one. That makes a bipartisan deal even less likely, at least before the elections.
That means the battle will probably produce little more than fodder for campaign advertising. Both sides' lobbying reflects the low odds of a law being enacted, with scant advertising and few signs of all-out campaigns that typify major Washington battles.
Read More Minimum wage debate insane, says 'Mr. Wonderful'
"It's really a matter of just making sure there are no surprises in what we view as a political vote," said Rob Green, executive director of the National Council of Chain Restaurants, a leading foe of the proposed increase.
The pressure for congressional action is further reduced by the states - 21 have minimum wages above $7.25. Five have enacted increases so far in 2014, and 29 others are considering boosts. By law, workers covered by both the federal and a state's minimum wage are entitled to the higher amount.
For Democrats, the minimum wage is the latest attempt to rouse traditional party supporters with Senate votes this election season.
They won passage of a measure this month extending expired benefits for the long-term unemployed, though it faces tough odds in the House. GOP senators thwarted another bill aimed at narrowing the pay gap between men and women.