Democrats introduced a bill Wednesday to gradually raise the federal minimum wage to $15 per hour, a long-shot plan that comes as the party tries to bill itself as a champion of the working class.

The proposal to hike the U.S. wage floor from the current $7.25 will likely fail in the GOP-held Senate even if it gets through the Democratic-controlled House. However, the new House Democratic majority sees the measure as a message that it wants to lift low-wage workers and boost the economy — and an effort to focus on its policy priorities amid the longest government shutdown ever.