And they should be. This is the first time since 1984 that the Republican Party presidential nominee has come into the convention leading in the polls.
Sixty-eight percent of Republican delegates interviewed for a CBS News/New York Times Delegate Survey said the Texas governor is the favorite to carry their home state in the presidential election.
Just 3 percent said they are supporting Bush only because he is the party's nominee.
Some of this enthusiasm gets generated at every convention. Even in 1996, when some polls showed Bill Clinton leading Bob Dole by more than 20 points at the start of the Republican convention, half the delegates said that they thought Dole would carry their state.
But even enthusiasm has its limits. And the delegate survey shows some potential pitfalls for the Bush campaign.
First off, many McCain delegates to the convention are not yet completely on board the Bush bus. That's especially true for delegates from the New England states that McCain carried in the primary - Rhode Island, Massachusetts, New Hampshire and Connecticut.
Second, there are delegates who even at this heady time for Republicans admit their states should rightly be placed in Gore's electoral vote column. Majorities of delegates in the District of Columbia, Hawaii, Maryland, Massachusetts, New York, Rhode Island and Vermont say Gore is clearly the favorite back home. In nine other states - California, Connecticut, Illinois, Iowa, Minnesota, New Jersey, New Mexico, Oregon and Tennessee - most delegates put the state in the toss-up column.
Finally, even the most enthusiastic delegates see potential Bush weaknesses and it's clear this convention is meant to assuage those doubts.
The two most frequently mentioned Bush weaknesses are related to experience - or more precisely, the lack of it. One in 10 delegates think Bush's greatest weakness is a general lack of experience, while 12 percent say it is specifically his lack of foreign policy experience.
National polls confirm that weakness. Fewer than half of voters in the most recent CBS News poll said they were confident in Bush's ability to handle an international crisis. The poll was conducted after Bush named former Secretary of Defense Dick Cheney as his running mate.
So it's no surprise that large portions of the convention agenda aim to bolster Bush's foreign policy profile. Retired Gen. Colin Powell was the star of Monday's proceedings. He praised Bush and Cheney, the man "with whom I shared many difficult days and nights during Desert Storm and other crises."
As of now, Bush's voters outside the convention hall haven't yet caught the GOP delegates' excitement for their candidate. Nationally, just 40 percent of Bush's voters say they are enthusiastically supportng him. Most still have reservations.
The success of this convention will be measured by the polls in the days and weeks ahead. Will Bush's voters catch some of the delegates' enthusiasm? And will Bush finally win the public's trust on matters of foreign policy?