As the deadline looms for Congress to fund the federal government, the House Republican freshmen who rode into office on a tidal wave of small-government, anti-spending support last year may face a new predicament: stick with the voters who got you elected -- many of whom are now calling for a government shutdown -- or agree to a compromise with Democrats who are fighting cuts.

The continuing congressional resolution on which the government is currently operating expires on March 4 -- meaning lawmakers need to make a decision, fast, about how to fund the government. On Wednesday, House Speaker John Boehner proposed a temporary funding bill that would keep the government up and running for two weeks after the deadline - and would include a $4 billion spending cut.

Senate Minority Leader Harry Reid roundly rejected the idea Wednesday night.

"Enacting these draconian cuts over two weeks would mean immediate, devastating impacts to the health of our economy and the safety of our communities," Reid's spokesman said in a release. Boehner's proposal came just a day after Reid announced that Senate Democrats would try to pass a 30-day extension that would keep the spending frozen at last year's levels.

But while Democrats and Republicans battle over the budget on Capitol Hill, freshmen Republicans may face another battle back at home. Several members, freshly returned to their districts during this week's Presidents Day recess, are hearing from their constituents at town hall meetings, and not everyone is ready for compromise.

Rep. Allen West, a Republican freshman from Florida, told Politico that after holding a town-hall meeting in Pompano Beach, his constituents' message was to stand tough,

"There's a very good possibility that government will shut down. I know the Democrats have their talking points lined up. They'll blame us for everything. What will we do?" West wondered.

And fellow Florida GOP freshmen Dan Webster said after hosting his own meeting in Winter Garden that the attendees assured him, "if we have to shut the government down, don't believe those polls you get out of the media. The people are behind you."

Both West and Webster unseated Democratic incumbents in 2010, part of a wave of support for a smaller-government, lower-spending agenda in the swing state. But freshmen representatives in other states are facing similar music back home.

Rep. Rob Woodall, R-Ga., arrived just in time for a town hall meeting in Monroe on Saturday, fresh off a 4:00 a.m. vote in the House that called for $61 billion in cuts for the remaining seven months of the fiscal year. But some in the audience were not completely satisfied and cheered the idea of the federal government shutting down if the Senate doesn't approve the House plan.

But the local paper, the Walton Tribune, says Woodall cautioned the audience against the idea of a shutdown.

"If we default on our loans, we would be dealing with skyrocketing interest rates," he told the crowd. "When the government was shut down in 1995 by Newt Gingrich, the people were behind him then too - in the beginning - but that changed."

Rep. Bill Flores, R-Texas, heard talk of a government shutdown at a Wednesday town hall in Waco. A local television station says cheers erupted when a Tea Party representative gave the congressman a rubber stamp that said, "Denied by taxpayers - insufficient funds."

But like his freshmen counterparts, Flores was also cautious about a possible shutdown. "This isn't an issue of brinkmanship," he said. "The House did its job, we're waiting for the rest of government to do its job."

Both the House and the Senate come back in session next week and will have less than a week to hammer out a solution before the current spending legislation expires.

Boehner has said that he wants to avoid a government shutdown -- which could mean that GOP leaders may be forced to concede some of the larger cuts Republicans have proposed. It also may mean that the many freshmen who rode into Congress last year with promises of draconian spending cuts may face a tough conversation with their fervent constituents.