As Americans go to the polls on Tuesday they are voting in what Joe Biden has framed as a vital test for American democracy in the face of a Republican party fielding candidates who buy into the big lie of a stolen 2020 election.

Republicans, meanwhile, have tried to capitalize on widespread economic anxiety in the face of rising inflation as well as stoking culture war themes and fears over crime, often spilling over into racism and intolerance.

Millions of voters are casting their ballot as Republicans and Democrats fight for control of Congress, numerous state governorships as well as many local offices and ballot initiatives on issues like abortion.

A handful of general scenarios could play out, each having momentous significance for the Biden presidency and the tactics of a resurgent Republican party and its de facto leader Donald Trump.

Republicans win the House, Democrats hold the Senate

In a split decision, expect Republicans to thwart Biden’s legislative agenda and launch a flurry of congressional investigations, for example into the botched military withdrawal from Afghanistan and the president’s son Hunter’s business dealings in China and Ukraine. Trump ally Jim Jordan might take the lead.

A Republican majority would also doom the House select committee investigating the January 6 attack on the US Capitol. They might even seek revenge by launching a counter-investigation into telecom companies that handed over phone records to the committee or into members of the panel themselves.

Policy-wise, Republicans could seek to reverse some major accomplishments of Biden’s first two years, such as climate spending, student loan forgiveness and corporate tax increases.

Kevin McCarthy, the House minority leader and current favourite to become House speaker, has told Punchbowl News that Republicans would use a future battle over raising the national debt ceiling as leverage to force cuts in public spending.

McCarthy has also warned that the party will not write a “blank cheque” for Ukraine, while Marjorie Taylor Greene, expected to be a prominent figure in the Republican caucus, told a rally in Iowa: “Under Republicans, not another penny will go to Ukraine. Our country comes first.”

But a Democratic-controlled Senate would be able to continue rubber-stamping Biden’s nominations for cabinet secretaries and federal judges.

Republicans win House and Senate

Despite polarisation in Washington, Biden has so far achieved some bipartisan victories on infrastructure, gun safety, health benefits for veterans and manufacturing investments to compete with China. But Republicans would be less likely to allow him further wins as the next presidential election draws closer.

Instead, expect a new antagonism between the White House and Congress. A Republican-controlled Senate could slow down or block Biden’s judicial nominees, including if there is an unexpected opening on the supreme court.

Conversely, Republican attempts to harden rules on immigration, gun rights or ban transgender women from playing in women’s sports would surely be met by a Biden presidential veto.

The Republican policy agenda remains nebulous. Mitch McConnell, the Republican minority leader in the Senate, has resisted publishing a platform, fuelling criticism that the party has a cult of personality around Trump.

Former president Barack Obama told a recent rally in Atlanta, Georgia: “These days, right now, just about every Republican politician seems obsessed with two things: owning the libs and getting Donald Trump’s approval.”

Rick Scott, chairman of the National Republican Senatorial Committee, did publish a 12-point plan that includes forcing poorer Americans who do not currently pay income tax to do so and reauthorising social security and Medicare every five years instead of allowing the programmes to continue automatically.

And Senator Lindsey Graham of South Carolina introduced a bill to create a national ban on abortions at 15 weeks, dividing Republicans and infuriating progressive activists. If far-right members put it to a vote, Senate Democrats would be sure to filibuster it.

The White House, meanwhile, would be forced on the defensive against a slew of congressional investigations into Afghanistan, Hunter Biden and other targets.

Democrats hold House and Senate

This would be a huge surprise and defy historical trends. Opinion pollsters would be crying into their beer, fearing that their industry is well and truly broken.

A Democratic sweep would give Joe Biden a mandate to enact a sweeping agenda that would again invite comparisons with former presidents Franklin Roosevelt and Lyndon Johnson.

Biden said last month that, if Democrats win control of Congress, the first bill he sends to Capitol Hill next year would codify Roe v Wade, the 1973 supreme court decision that overturned the constitutional right to abortion. The party could also push for national protections for same-sex marriage and voting rights.

The president wants further actions on gun safety including a ban on assault weapons. He could seek to resurrect elements of his Build Back Better agenda, including more climate measures and expanding the social safety net, and make another attempt to tackle racial discrimination in policing.

And some Democrats are drafting legislation to prevent Trump from running for president in 2024 due to his instigation of the January 6 insurrection, the New York Times reported, although that would be a long shot.

But much would depend on how big – or small – the Democratic majority turns out to be. If it is slender, the conservative Democrats Joe Manchin of West Virginia and Kyrsten Sinema of Arizona could once again call the shots and frustrate the president’s ambitions.