By Trevor Hunnicutt

WASHINGTON (Reuters) - Buoyed by a string of legislative victories, Democrats and their allies are throwing money at key congressional races hoping to overcome President Joe Biden's poor approval ratings, high inflation, and historical precedent in the November midterm elections.

In the coming days, millions of dollars will flow into congressional races from groups outside the Democratic Party to tout Biden's $430 billion climate, healthcare and tax bill called the "Inflation Reduction Act," aides and allies to Biden tell Reuters.

Climate, health and pro-Biden groups will target voters in swing districts with television, radio, and internet ads, rallies, and bus tours. Some will even knock on doors.

Midterms are difficult for the party holding power even in normal years, but through history inflation has been especially damaging for incumbents. It hit 40-year highs under Biden and voters say the economy is their top concern.

Still, Biden advisers are increasingly optimistic voters will punish Republicans for opposing the inflation bill, which Biden will sign on Tuesday, and for their party's attacks on abortion rights.

Already, the Democratic Party has spent $535 million in ads for the general election, while Republicans have spent $423 million, AdImpact research showed last month. While funding for outside groups is opaque, top party contributors include several billionaires, such as hedge fund creator David Shaw, LinkedIn founder Reid Hoffman and venture capitalist John Doerr, federal filings show.

Outside campaigns will be bolstered by Democratic Party spending and 35 trips to 23 states by Biden and his Cabinet through the end of August to tout the bill.

'Momentum Shifting'

"This is as strong an August environment for an incumbent president and his party as you can imagine in terms of getting things done and the momentum shifting," said senior Biden adviser Steve Ricchetti.

Polling and forecasts are not on their side.

Six in ten voters either have never heard of the latest bill or know next to nothing about it, according to a Reuters/Ipsos poll conducted earlier this month. Only 40 percent of Americans approve of Biden's performance, according to a Reuters/Ipsos opinion poll completed last Tuesday.

All 435 House seats and a third of the 100-member Senate are up for grabs in November. Both chambers are narrowly controlled by Democrats, and traditionally midterms favor the party not in the White House. Most forecasters give Republicans a strong chance of taking the House and see the Senate as up for grabs.

Republicans say the Democrats' strategy is delusional given Biden's poll numbers and predictions that the inflation bill will have only modest short-term impact on prices.

But Democrats say they're not seeing blistering voter opposition to the inflation bill, compared to Obamacare in 2010, which ushered in a Republican landslide.

"Every single Democrat who's running for Congress is going to run ads on this and talk about this," said Anne Shoup, a spokesperson for Protect Our Care, a healthcare advocacy group targeting Republicans who oppose the inflation bill.

'Pro-Polluter' Republicans Targeted

Building Back Together, a non-profit run by former Biden campaign advisers, has a television, digital and radio ads plan as does the Democratic National Committee, which is focusing on Black, Latino and Asian voters.

The League of Conservation Voters, an environmental advocacy, launched a $2.2 million advertising campaign to thank Democratic supporters of the inflation bill; Climate Action Campaign plans digital ads thanking 24 lawmakers who voted for the bill.

League-affiliated organizers will also spend $13 million on a door-to-door campaign about the bill and how candidates voted in seven political battleground states. Ads in the coming weeks will cast Republicans who opposed the bill as "pro-polluter," said spokesperson Emily Samsel.

The Hub Project, an outside group focused on populist economic messaging, is targeting four Republicans who opposed the bill: Representative David Valadao of California, Ashley Hinson of Iowa, Don Bacon of Nebraska, and Nicole Malliotakis of New York.

Cook Political Report earlier this month downgraded the chances of victory for Bacon and Malliotakis but the targeted campaigns expressed no concern.

"The only thing that will give Iowa families relief from Democrat induced runaway inflation, tax increases and back breaking increases on gas and groceries is a Republican Majority in Congress," said Sophie Crowell, Hinson's campaign manager.

(Reporting by Trevor Hunnicutt; editing by Heather Timmons and Josie Kao)