The new House Republican majority will look to set the tone for the next session of Congress with the first bill it offers this week.

Incoming Speaker John Boehner (Ohio) and the GOP leadership have an opportunity to send a signal about their priorities in the next Congress when they introduce H.R. 1, the first formal piece of legislation of their new majority.

Republicans have several options to choose from when they decide which priorities to advance in the opening days of the next Congress.

The GOP has made no secret of its plan to hold a vote on the repeal of President Obama's healthcare reform law. Rep. Fred Upton (R-Mich.), the incoming chairman of the House Energy and Commerce Committee, said this weekend that such a vote would come before the State of the Union address. That vote could be among the first of the Boehner-led House.

Republicans have also promised to focus on making significant cuts to government spending. Boehner has made a point so far of keeping festivities associated with the Republican takeover of the House at a minimum, in a bow toward the sense of frugality the GOP thinks voters want in Washington.

The new Speaker told CBS last month that he planned to cut budgets for himself and every House lawmaker by 5 percent — a sign of belt-tightening by the new Congress. A vote on that could help set the tone of "austerity" Boehner has reportedly looked to set with his new majority.

Those types of bills, along with several others, are under consideration for a busy first few days of the new Congress, which begins after members are sworn in on Wednesday, Jan. 5.

The first piece of legislation introduced in a new session of Congress has typically enjoyed success in becoming law.

When Democrats retook control of the House and Senate in the 2006 elections, Speaker Nancy Pelosi (D-Calif.) made her H.R. 1 a bill to implement the findings of the 9/11 Commission. And after President Obama took office in early 2009, H.R. 1 was the stimulus act, a piece of legislation that became a signature component of Democrats' economic plans.

Speaker Dennis Hastert (R-Ill.) introduced controversial legislation to expand Medicare's prescription drug benefit as his H.R. 1 during the 108th Congress, though he didn't introduce the legislation until June 25 — well after a new batch of lawmakers had been sworn in.

Boehner also has experience in shepherding an H.R. 1 through Congress from the 107th Congress. He was the principal sponsor of the No Child Left Behind Act, President George W. Bush's education bill, which faces a congressional battle for reauthorization.