President Bush will make a rare visit to the Capitol today to lobby lawmakers who are undecided on the Central America Free Trade Agreement even as House GOP vote-counters grow increasingly confident that they will have the votes to pass one of the White House’s signature domestic initiatives tonight.

Bush’s trip to this morning’s Republican Conference meeting — to be followed by a visit from Vice President Cheney for one-on-one Member lobbying this afternoon — underscores the high stakes being attached to the CAFTA vote by both sides in the fight, as the administration pushes to increase support for the bill and Democratic leaders and organized labor work to defeat it.

“Our Members need to hear from the president about why its important to pass CAFTA,” said Ron Bonjean, spokesman for Speaker Dennis Hastert (R-Ill.). “Having the President of the United States on the Hill is a great way to communicate to Members that this is highly important to the administration and the Republican Congress.”

News of Bush’s visit came as Republicans became optimistic enough Tuesday to make plans for a vote on final passage tonight. Earlier in the week, the vote looked likely to slip to Thursday or Friday, but as GOP leaders intensified their lobbying effort Tuesday they became convinced that support for the measure was growing and that they should strike while the iron is hot.

While they are cautiously optimistic, Republican lawmakers involved in building CAFTA support predicted that this floor showdown would be similar to the 2001 Trade Promotion Authority vote and the 2003 Medicare prescription drug measure fight. In those cases, the vote was held open beyond the allotted time as both sides held back votes and bartered for support.

“I’ve seen them go to the floor with worse whip counts and win,” said a Member who is part of the Republican Whip team.

That optimism grew during a blizzard of activity Tuesday, as both supporters and opponents of the trade bill staged high-profile press events and attempted to sway the rapidly dwindling pool of undecided lawmakers.

Hastert held a press conference with a group of Hispanic leaders to tout CAFTA, arguing that “this two-lane highway of trade will lead to economic prosperity for the United States.”

On the other side of the issue, a group of Democrats joined by a handful of Republicans opposed to the agreement spoke out on the West Lawn of the Capitol Tuesday morning, and another group of conservative Republican opponents gathered for their own media event at noon.

Behind the scenes, Republican leaders attempted to chip away at the distance between their current, closely-guarded vote count and the 218 necessary for passage.

That effort encountered a small hiccup Tuesday, when a bill designed to toughen enforcement of rules governing trade with China failed to garner the two-thirds support necessary for passage under suspension of the rules.

Democrats mostly voted against the measure, sponsored by Rep. Phil English (R-Pa.), as a protest against the GOP’s use of the issue to try to round up more support for CAFTA. But Republican leaders plan to bring the bill back to the floor today under regular order and it is expected to pass easily, given that it received 240 votes Tuesday.

While the English bill has helped to assuage many lawmakers’ concerns about China and the Bush administration has negotiated a series of side agreements to placate lawmakers from textile-producing districts, pockets of Republican opposition remain among Members from sugar-producing states and from Members with strong support from organized labor.

Seeking to counter those objections, supporters of the measure have convened a series of outreach meetings, including a gathering of key Members with Hastert last night and scheduled meetings of the outside lobbying coalition this morning and the Whip task force later today.

The visits by Bush and Cheney could help persuade some of the remaining CAFTA holdouts, who are looking for reassurances that the administration will address their individual concerns. When announcing the president’s schedule for this week, White House officials made clear that it was purposely uncluttered so as to allow him maximum flexibility to meet with Members of Congress.

While the Bush administration works on Republicans, the outside lobbying coalition’s efforts are particularly important to securing the support of Democrats, who have faced strong peer pressure within their party to vote against the agreement. Republican vote-counters began the week hoping to convince 17 to 20 Democrats to vote yes, though some GOP leadership aides have wondered privately whether they will ultimately attract that many.

In his weekly session with reporters Tuesday, House Minority Whip Steny Hoyer (D-Md.) predicted that “the overwhelming number of Democrats are going to vote against CAFTA.”

While he did not say he expected the bill to be defeated, Hoyer noted that Republicans were being forced to cut a number of side agreements in order to secure adequate support for the bill on their own side of the aisle.

The pressure continued to mount on the Democratic side Tuesday as 20 leading labor groups — themselves in disarray after the decision earlier this week by four unions to split from the AFL-CIO — increased pressure on the Democratic leadership to keep their Caucus unified in opposition to CAFTA.

The unions vowed in a letter to Democratic leaders Tuesday to withhold financial help for vulnerable House incumbents who vote for the measure, specifically pointing to Democratic Reps. Jim Matheson (Utah), Dennis Moore (Kansas) and Melissa Bean (Ill.).

“Our work to help elect at-risk Members, at your urging, will not extend to those who vote against us on this issue,” the unions wrote. “As such, we hope that you will also convey to them that we believe those who receive our support have an obligation to vote with us on CAFTA. Further, we ask that the [Democratic Congressional Campaign Committee] remove from Frontline status any member who votes wrong on CAFTA.”

“Simply put, there must be real and measurable consequences for opposing labor on this issue,” the letter said. “The stakes are too high for the workers of America. We cannot and we will not give any Democrat a pass on CAFTA.”

Democratic sources said the move angered leadership and Members, especially as the party works overtime to keep their Caucus aligned against the bill.

“It’s not helpful, to say the least,” said a Democratic leadership aide.

As is often the case with trade bills, the CAFTA issue has created some strange ideological bedfellows. Some staunch Republican conservatives plan to buck their party leadership, while the outside coalition has marshaled nearly equal numbers of high-profile Republican and Democratic lobbyists to gather support.

In between those two sides, moderate lawmakers in both parties are playing key roles. Ron Talley, the head of the moderate Republican Main Street Partnership, said he expected centrist GOP lawmakers to play a key role in whipping support from both Democrats and conservative Republicans.

“What we’re going to be trying to do is pick off as many Members as possible,” Talley said. “It’s going to be al little dual whipping — a whip to the left and a whip to the right.”

Erin P. Billings and Chris Cillizza contributed to this report.