In a legislative update titled “House GOP Fights Alone for American Energy,” House Republican Policy Committee Chairman Thaddeus McCotter (Mich.) accused the “wildly unpopular” president of throwing “them under the bone-dry bus” as he headed to China for the Olympics.

McCotter wrote that “Perhaps our Compassionate Conservative-in-Chief will bring our absent Democrat Congress some ‘Made in (communist) China’ souvenir t-shirts: ‘Bush went to Beijing and all I got was this lousy five week, paid vacation.’

Asked for comment, White House spokesman Tony Fratto said, "Let me be very clear: we support what the House Republicans are doing.  They are doing the right thing by shining a light on this issue.

There should be no mistake about that. Unfortunately, simply calling Congress into session isn't going to guarantee that Speaker [Nancy] Pelosi [D-Calif.] will give a vote on the bill.

Despite the friction with Bush, most believe the House Republican initiative has been a public relations success.

But as crowds grew sparse and the number of Republican staffers filling the gallery seats in the lower chamber dwindled on Tuesday, House GOP leaders became aware they will need to do something different to maintain the media’s interest in the demonstration.

A former aide to ex-House Speaker Dennis Hastert (R-Ill.) said the protest is working, but added that the biggest challenge for the GOP is figuring out a way to keep the momentum all month long.

Ron Bonjean, CEO of the Bonjean Company, said, “After this week, they may need to focus on paring back on the schedule to keep Republican members and the media interested, or else it becomes the law of diminishing press returns.”

And above all, Bonjean said, Republicans need to develop an exit strategy that allows them to end as they began — on a high note:  “Their exit strategy might be to have Republican members go on an energy [tour], visiting certain districts across the country and then finally wind[ing] up at an oil rig before the Republican convention.”

Another GOP strategist said that no matter when the protest concludes, Republicans have already succeeded in bringing attention to one of the few issues Democrats have struggled with since the 2006 takeover.

“Issues, no matter how important, are only truly effective when they highlight a larger theme,” said Stuart Roy, a partner at Prism Public Affairs and former aide to then-Majority Leader Tom DeLay (R-Texas). Roy also contributes to The Hill’s Pundits Blog.

Rep. Marilyn Musgrave (R-Colo.), a top Democratic target this cycle, said she has been the beneficiary of positive local coverage for returning to D.C., but said she is assessing her availability “hour-by-hour.”

“It’s a hard choice. I do have a tough race at home [and] I want to be working in my district, but I feel strongly about this issue,” Musgrave said.

Rep. Jean Schmidt (R-Ohio), who defeated Democrat Victoria Wulsin by one percentage point in 2006, said she thinks that taking part in the GOP protest will pay dividends in November, regardless of whether it takes away from time in her district.

“I think the folks of the 2nd district want me here. I am here to work for them,” Schmidt said.

She will face Wulsin again in November.

Sam Youngman contributed to this article.