A government shutdown is not in the Republican Party's self-interest, a top GOP senator said Tuesday.

Sen. Lindsey GrahamLindsey Olin GrahamThe Hill's 12:30 Report — Sponsored by Delta Air Lines — GOP centrists in striking distance of immigration vote Dem leaders request bipartisan meeting on Russia probe Senate GOP urges Trump administration to work closely with Congress on NAFTA MORE (R-S.C.) suggested that the party should accept a compromise proposal on funding the government through the end of this fiscal year in order to avert a potentially damaging shutdown.

"I don't think a government shutdown is politically in the Republican Party's interest," Graham said during an interview on WVOC Radio in South Carolina.

The center-right senator's comments came after House Republicans raised the stakes in negotiations with Democrats by ruling out another stopgap spending measure.

That would force both sides to come together on a long-term proposal before April 8, when the current short-term funding bill is set to expire.

Graham indicated it would be wise for Republicans to accept "70 to 80 percent" of what they want this year, which would allow lawmakers to take up a 2012 budget in which they could make further cuts.

"What is in our interest is to be the party that is making hard decisions like you do at home," the senator said. "If we stay on message there and ask for reasonable things to get this reducing government started in 2011, I think we will do well in 2012. If the Democrats come 70 to 80 percent our way, as Ronald Reagan said, that's a pretty good deal. We'll get the 20 to 30 percent later."

But House Minority Whip Steny Hoyer (D-Md.) said Tuesday the likelihood of a shutdown has increased due to the impasse of a long-term plan on Capitol Hill and Graham said negotiators are "not close to that number yet."

And in preparation for a potential shutdown, both sides have assigned preemptive blame to one another should the government cease operations.

Some political observers have said that Republicans could take the brunt of the blame for a shutdown like they did the last time one occurred in the mid-1990s, when they controlled the House and Senate. But others say that voters could blame Democrats since they control the Senate and White House.

Contrary to Graham, some conservative GOP lawmakers backed by Tea Party activists have suggested that a shutdown could be neccessary to drive home the party's message on spending.

Graham faces reelection in 2014, and some campaign observers predict he could face a conservative primary challenger.